Готові списки джерел за темами / Dimension de Hausdorff

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Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 4 травня 2024

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Статті в журналах з теми "Dimension de Hausdorff"

Myjak, Józef. "Some typical properties of dimensions of sets and measures." Abstract and Applied Analysis 2005, no. 3 (2005): 239–54. http://dx.doi.org/10.1155/aaa.2005.239.

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This paper contains a review of recent results concerning typical properties of dimensions of sets and dimensions of measures. In particular, we are interested in the Hausdorff dimension, box dimension, and packing dimension of sets and in the Hausdorff dimension, box dimension, correlation dimension, concentration dimension, and local dimension of measures.

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Conidis, Chris J. "A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one." Journal of Symbolic Logic 77, no. 2 (June 2012): 447–74. http://dx.doi.org/10.2178/jsl/1333566632.

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AbstractRecently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via [10. 3. 7] that every real of strictly positive effective Hausdorff dimension computes reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one).

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Leonov, G. "Hausdorff–Lebesgue Dimension of Attractors." International Journal of Bifurcation and Chaos 27, no. 10 (September 2017): 1750164. http://dx.doi.org/10.1142/s0218127417501644.

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Definitions of Hausdorff–Lebesgue measure and dimension are introduced. Combination of Hausdorff and Lebesgue ideas are used. Methods for upper and lower estimations of attractor dimensions are developed.

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DAS, TUSHAR, LIOR FISHMAN, DAVID SIMMONS, and MARIUSZ URBAŃSKI. "Badly approximable points on self-affine sponges and the lower Assouad dimension." Ergodic Theory and Dynamical Systems 39, no. 3 (June 20, 2017): 638–57. http://dx.doi.org/10.1017/etds.2017.42.

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We highlight a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of badly approximable points that lie in certain non-conformal fractals, known as self-affine sponges, is bounded below by the dynamical dimension of these fractals. For self-affine sponges with equal Hausdorff and dynamical dimensions, the set of badly approximable points has full Hausdorff dimension in the sponge. Our results, which are the first to advance beyond the conformal setting, encompass both the case of Sierpiński sponges/carpets (also known as Bedford–McMullen sponges/carpets) and the case of Barański carpets. We use the fact that the lower Assouad dimension of a hyperplane diffuse set constitutes a lower bound for the Hausdorff dimension of the set of badly approximable points in that set.

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ZÄHLE, M. "THE AVERAGE FRACTAL DIMENSION AND PROJECTIONS OF MEASURES AND SETS IN Rn." Fractals 03, no. 04 (December 1995): 747–54. http://dx.doi.org/10.1142/s0218348x95000667.

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In this note we introduce the concept of local average dimension of a measure µ, at x∈ℝn as the unique exponent where the lower average density of µ, at x jumps from zero to infinity. Taking the essential infimum or supremum over x we obtain the lower and upper average dimensions of µ, respectively. The average dimension of an analytic set E is defined as the supremum over the upper average dimensions of all measures supported by E. These average dimensions lie between the corresponding Hausdorff and packing dimensions and the inequalities can be strict. We prove that the local Hausdorff dimensions and the local average dimensions of µ at almost all x are invariant under orthogonal projections onto almost all m- dimensional linear subspaces of higher dimension. The corresponding global results for µ and E (which are known for Hausdorff dimension) follow immediately.

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Urbański, Mariusz. "Transfinite Hausdorff dimension." Topology and its Applications 156, no. 17 (November 2009): 2762–71. http://dx.doi.org/10.1016/j.topol.2009.01.025.

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J�rgensen, H., and L. Staiger. "Local Hausdorff dimension." Acta Informatica 32, no. 5 (August 1, 1995): 491–507. http://dx.doi.org/10.1007/s002360050025.

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Jürgensen, H., and L. Staiger. "Local Hausdorff dimension." Acta Informatica 32, no. 5 (May 1995): 491–507. http://dx.doi.org/10.1007/bf01213081.

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SIMMONS, DAVID. "A Hausdorff measure version of the Jarník–Schmidt theorem in Diophantine approximation." Mathematical Proceedings of the Cambridge Philosophical Society 164, no. 3 (April 5, 2017): 413–59. http://dx.doi.org/10.1017/s0305004117000214.

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AbstractWe solve the problem of giving sharp asymptotic bounds on the Hausdorff dimensions of certain sets of badly approximable matrices, thus improving results of Broderick and Kleinbock (preprint 2013) as well as Weil (preprint 2013), and generalising to higher dimensions those of Kurzweil ('51) and Hensley ('92). In addition we use our technique to compute the Hausdorfff-measure of the set of matrices which are not ψ-approximable, given a dimension functionfand a function ψ : (0, ∞) → (0, ∞). This complements earlier work by Dickinson and Velani ('97) who found the Hausdorfff-measure of the set of matrices which are ψ-approximable.

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SHANG, LEI, and MIN WU. "SLOW GROWTH RATE OF THE DIGITS IN ENGEL EXPANSIONS." Fractals 28, no. 03 (May 2020): 2050047. http://dx.doi.org/10.1142/s0218348x20500474.

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We are concerned with the Hausdorff dimension of the set [Formula: see text] where [Formula: see text] is the digit of the Engel expansion of [Formula: see text] and [Formula: see text] is a function such that [Formula: see text] as [Formula: see text]. The Hausdorff dimension of [Formula: see text] is studied by Lü and Liu [Hausdorff dimensions of some exceptional sets in Engel expansions, J. Number Theory 185 (2018) 490–498] under the condition that [Formula: see text] grows to infinity. The aim of this paper is to determine the Hausdorff dimension of [Formula: see text] when [Formula: see text] slowly increases to infinity, such as in logarithmic functions and power functions with small exponents. We also provide a detailed analysis of the gaps between consecutive digits. This includes the central limit theorem and law of the iterated logarithm for [Formula: see text] and the Hausdorff dimension of the set [Formula: see text] where [Formula: see text] with the convention [Formula: see text].

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Дисертації з теми "Dimension de Hausdorff"

Mucheroni, Laís Fernandes [UNESP]. "Dimensão de Hausdorff e algumas aplicações." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151653.

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Intuitivamente, um ponto tem dimensão 0, uma reta tem dimensão 1, um plano tem dimensão 2 e um cubo tem dimensão 3. Porém, na geometria fractal encontramos objetos matemáticos que possuem dimensão fracionária. Esses objetos são denominados fractais cujo nome vem do verbo "frangere", em latim, que significa quebrar, fragmentar. Neste trabalho faremos um estudo sobre o conceito de dimensão, definindo dimensão topológica e dimensão de Hausdorff. O objetivo deste trabalho é, além de apresentar as definições de dimensão, também apresentar algumas aplicações da dimensão de Hausdorff na geometria fractal.
We know, intuitively, that the dimension of a dot is 0, the dimension of a line is 1, the dimension of a square is 2 and the dimension of a cube is 3. However, in the fractal geometry we have objects with a fractional dimension. This objects are called fractals whose name comes from the verb frangere, in Latin, that means breaking, fragmenting. In this work we will study about the concept of dimension, defining topological dimension and Hausdorff dimension. The purpose of this work, besides presenting the definitions of dimension, is to show an application of the Hausdorff dimension on the fractal geometry.

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Reeve, Russell Lynn. "Estimating the Hausdorff dimension." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/37744.

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Spear, Donald W. "Hausdorff, Packing and Capacity Dimensions." Thesis, University of North Texas, 1989. https://digital.library.unt.edu/ark:/67531/metadc330990/.

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In this thesis, Hausdorff, packing and capacity dimensions are studied by evaluating sets in the Euclidean space R^. Also the lower entropy dimension is calculated for some Cantor sets. By incorporating technics of Munroe and of Saint Raymond and Tricot, outer measures are created. A Vitali covering theorem for packings is proved. Methods (by Taylor and Tricot, Kahane and Salem, and Schweiger) for determining the Hausdorff and capacity dimensions of sets using probability measures are discussed and extended. The packing pre-measure and measure are shown to be scaled after an affine transformation. A Cantor set constructed by L.D. Pitt is shown to be dimensionless using methods developed in this thesis. A Cantor set is constructed for which all four dimensions are different. Graph directed constructions (compositions of similitudes follow a path in a directed graph) used by Mauldin and Willjams are presented. Mauldin and Williams calculate the Hausdorff dimension, or, of the object of a graph directed construction and show that if the graph is strongly connected, then the a—Hausdorff measure is positive and finite. Similar results will be shown for the packing dimension and the packing measure. When the graph is strongly connected, there is a constant so that the constant times the Hausdorff measure is greater than or equal to the packing measure when a subset of the realization is evaluated. Self—affine Sierpinski carpets, which have been analyzed by McMullen with respect to their Hausdorff dimension and capacity dimension, are analyzed with respect to their packing dimension. Conditions under which the Hausdorff measure of the construction object is positive and finite are given.

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Serantola, Leonardo Pereira. "Dimensão generalizada de Hausdorff /." São José do Rio Preto, 2019. http://hdl.handle.net/11449/191015.

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Orientador: Márcio Ricardo Alves Gouveia
Resumo: O presente trabalho trata de conceitos relacionados com a medida generalizada de Hausdorff, onde o principal objetivo consiste na obtenção de conjuntos cuja dimensão seja um número positivo não inteiro. Ele começa com uma definição sobre as propriedades que uma função de conjunto deve satisfazer para ser considerada uma medida de Carathéodory, suas implicações e consequências. Após a explicação destes conceitos iniciais, dá-se alguns exemplos de funções de conjunto contínuas e monótonas com a apresentação da função de escala logarítmica, que é peça chave para o desenvolvimento de conjuntos de medidas positivas não inteiras, além da introdução da medida de Hausdorff com seus desdobramentos. Algumas hipóteses sobre funções côncavas são apresentadas juntamente com fórmulas deduzidas com bases nestas hipóteses e na concavidade da função. Utiliza-se a função de escala logarítima para a determinação da dimensão de vários conjuntos, inclusive o conjunto de Cantor. Posteriormente, há uma adaptação dos conceitos trabalhados para o tratamento de dimensões relacionadas à números diádicos irracionais. Por fim, os conceitos tratados sobre a reta real são estendidos para produtos cartesianos, com especial enfoque para conjuntos planares.
Abstract: The present work deals with concepts related to the generalized Hausdorff measure, where the main objective is to obtain sets whose dimension is a positive non integer number. It begins with a definition of the properties that a set function must satisfy to be considered a Carathéodory measure, their implications and consequences. Following the explanation of these initial concepts, some examples of continuous and monotonous set functions are given with the presentation of the logarithmic scale function, which is key to the development of non-integer positive measure sets, in addition to the introduction of the Hausdorff measure with its developments. Some assumptions about concave functions are presented together with formulas derived from these assumptions and the concavity of the function. The logarithmic scale function is used to determine the dimension of various sets, including the Cantor set. Later, there is an adaptation of the concepts worked for the treatment of dimensions related to irrational dyadic numbers. Finally, the concepts treated on the real line are extended to Cartesian products, with special focus on planar sets.
Mestre

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Dufloux, Laurent. "Dimension de Hausdorff des ensembles limites." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD022/document.

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Soit G le groupe SO°(1, n) (n ≥ 3) ou PU(1, n) (n ≥ 2) et fixons une décomposition d'Iwasawa G = KAN. Soit ɼ un sous-groupe discret de G, que nous supposons Zariski-dense et de mesure de Bowen-Margulis-Sullivan finie. Lorsque G = SO°(1, n), nous étudions la géométrie de la mesure de Bowen-Margulis-Sullivan le long des sous-groupes fermés connexes de N, en lien avec la dichotomie de Mohammadi-Oh. Nous établissons des résultats déterministes sur la dimension des projections de la mesure de Patterson- Sullivan. Lorsque G = PU(1, n), nous relions la géométrie de la mesure de Bowen- Margulis-Sullivan le long du centre du groupe de Heisenberg au problème du calcul de la dimension de Hausdorff de l'ensemble limite relativement à la distance sphérique au bord. Nous calculons cette dimension pour certains groupes de Schottky
Let G be the group SO° (1,n) (n ≥ 3) or PU(1, n) (n ≥ 2) and fix some Iwasawa decomposition G = KAN. Let ɼ be a discrete subgroup of G.We assume that ɼ is Zariski-dense with finite Bowen-Margulis-Sullivan measure. When G = SO°(1,n), we investigate the geometry of the Bowen-Margulis-Sullivan measure elong connected closed subgroups of N. This is related to the Mohammadi-Oh dichotomy. We then prove deterministic results on the dimension of projections of Patterson-Sullivan measure. When G = PU(1,n), we relate the geometry of Bowen-Margulis-Sullivan measure along the center of Heisenberg group to the problem of computing the Hausdorff dimension of the limit set with respect to the spherical metric on the boudary. We construct some Schottky subgroups for wich we are able to compute this dimension

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Zürcher, Thomas Zürcher Thomas. "Hausdorff dimension and regularity of Sobolev functions /." [S.l.] : [s.n.], 2009. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.

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Martin, Charles 1966. "Hausdorff dimension of harmonic measures in Rd." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=69764.

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In 1986, J. Bourgain showed that, for a given dimension d $ ge$ 2, there exists $ rho sb{d}$ $<$ d such that any harmonic measure in $ Re sp{d}$ is supported by a set of Hausdorff dimension at most $ rho sb{d}$.
This thesis presents a detailed and comprehensive exposition of Bourgain's theorem. Formal definitions of harmonic measures and Hausdorff dimensions are provided and all the required preliminary results about these concepts are rigorously proved. Generally speaking, the proof of the theorem itself is similar to the one originally presented by Bourgain. However, a more structured approach and an increased level of details make the argument easier to follow and understand.

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Siebert, Kitzeln B. "A modern presentation of "dimension and outer measure"." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1211395297.

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Satiracoo, Pairote. "Hausdorff dimension of attractors of infinitely renormalizable maps." Thesis, University of Warwick, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.400147.

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Brandão, Daniela Teresa Quaresma Santos. "Dimensões fractais e dimensão de correlação." Master's thesis, Universidade de Évora, 2008. http://hdl.handle.net/10174/17740.

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O objetivo deste trabalho é o estudo da dimensão fractal, nomeadamente a dimensão de Hausdorff, dimensão de capacidade e dimensão de correlação, relacionando-as e efetuando o cálculo em alguns exemplos. Sempre que se considera indispensável, são apresentadas noções introdutórias para uma melhor compreensão dos conceitos analisados. O Capítulo 2 é dedicado ao estudo da dimensão de Hausdorff, introduzindo, previamente, uma noção de medida, de Hausdorff. No Capítulo 3 analisamos a dimensão de capacidade, suas propriedades e inconvenientes, relacionando, no final, esta dimensão com a dimensão de Hausdorff. O Capítulo 4 estuda técnicas para calcular dimensões. São estudados subconjuntos de medida. Finita, sistemas de funções iteradas, conjuntos auto-semelhantes e auto-afins e dimensões de gráficos. O Capítulo 5 é dedicado à dimensão de correlação. Estuda o expoente de correlação  Introduzido por Grassberger e Procaccia. São analisadas funções de dimensão 1 e no plano. Terminamos com o estudo de séries temporais de variável única. ABSTRACT: The aim of this work is the study of the fractal dimension, namely the Hausdorff dimension, the box-counting dimension and the correlation dimension, relating and computing them in some examples. Everytime it is necessary we introduce the basic concepts to a better understanding of the concepts analysed in this work. Chapter 2 is dedicated to the study of the Hausdorff dimension, introducing first the notion of Hausdorff measure. Chapter 3 is concerned with the box-counting dimension, its properties and problems. Then we relate this dimension With Hausdorff dimension studied in Chapter 2. Chapter 4 is dedicated to the techniques for calculating dimensions. We study subsets of finite measure, iterated function schemes, self-similar and self-affine sets and dimensions of graphs. Finally, in Chapter 5 we present the correlation dimension. We study the correlation exponent, introduced by Grassberger and Procaccia. We finish this Chapter with a study of single-variable time series.

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Книги з теми "Dimension de Hausdorff"

1943-, Mauldin R. Daniel, and Williams S. C. 1952-, eds. The exact Hausdorff dimension in random recursive constructions. Providence, R.I., USA: American Mathematical Society, 1988.

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Graf, Siegfried. The exact Hausdorff dimension in random recursive constructions. Providence, R.I: American Mathematical Society, 1988.

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1972-, Tyson Jeremy T., ed. Conformal dimension: Theory and application. Providence, R.I: American Mathematical Society, 2010.

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Local dimensions of intersection measures: Similarities, linear maps and continuously differentiable functions. Helsinki: Suomalainen Tiedeakatemia, 2010.

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Paradoxes of measures and dimensions originating in Felix Hausdorff's ideas. Singapore: World Scientific, 1994.

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PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011 Messina, Italy). Fractal geometry and dynamical systems in pure and applied mathematics. Edited by Carfi David 1971-, Lapidus, Michel L. (Michel Laurent), 1956-, Pearse, Erin P. J., 1975-, Van Frankenhuysen Machiel 1967-, and Mandelbrot Benoit B. Providence, Rhode Island: American Mathematical Society, 2013.

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Fourier Analysis and Hausdorff Dimension. Cambridge University Press, 2015.

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Mattila, Pertti. Fourier Analysis and Hausdorff Dimension. Cambridge University Press, 2015.

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Mattila, Pertti. Fourier Analysis and Hausdorff Dimension. Cambridge University Press, 2015.

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Gu, Xiao-Ping. Hausdorff dimension of some invariant sets. 1992.

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Частини книг з теми "Dimension de Hausdorff"

Beardon, Alan F. "Hausdorff Dimension." In Iteration of Rational Functions, 246–56. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-4422-6_10.

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Edgar, Gerald A. "Hausdorff Dimension." In Undergraduate Texts in Mathematics, 147–94. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-4134-6_6.

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Walczak, Paweł. "Hausdorff dimension." In Dynamics of Foliations, Groups and Pseudogroups, 155–82. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7887-6_5.

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Schwartz, Richard. "Hausdorff dimension bounds." In Mathematical Surveys and Monographs, 131–37. Providence, Rhode Island: American Mathematical Society, 2014. http://dx.doi.org/10.1090/surv/197/19.

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Ferreira, Flávio, Alberto A. Pinto, and David A. Rand. "Hausdorff Dimension versus Smoothness." In Progress in Nonlinear Differential Equations and Their Applications, 195–209. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8482-1_15.

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Hausdorff, Felix. "Dimension und äußeres Maß." In Felix Hausdorff Gesammelte Werke, 19–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-59483-0_2.

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Bothe, Hans-Günther, and Jörg Schmeling. "Die Hausdorff-Dimension in der Dynamik." In Felix Hausdorff zum Gedächtnis, 229–52. Wiesbaden: Vieweg+Teubner Verlag, 1996. http://dx.doi.org/10.1007/978-3-322-80276-7_9.

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Charalambous, Michael G. "The Gaps Between the Dimensions of Normal Hausdorff Spaces." In Dimension Theory, 245–50. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22232-1_32.

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Flath, Dan, and Rhodes Peele. "Hausdorff Dimension in Pascal’s Triangle." In Applications of Fibonacci Numbers, 229–44. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2058-6_22.

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Staiger, Ludwig. "Kolmogorov complexity and Hausdorff dimension." In Fundamentals of Computation Theory, 434–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51498-8_42.

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Тези доповідей конференцій з теми "Dimension de Hausdorff"

Antonov, D., and J. E. F. T. Ribeiro. "Hausdorff dimension of quark trajectories from SCSB and confinement." In THE IX INTERNATIONAL CONFERENCE ON QUARK CONFINEMENT AND THE HADRON SPECTRUM—QCHS IX. AIP, 2011. http://dx.doi.org/10.1063/1.3574989.

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Takahashi, H. "Redundancy of universal coding, Kolmogorov complexity, and Hausdorff dimension." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228091.

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Pestana, Dinis D., Sandra M. Aleixo, and J. Leonel Rocha. "Hausdorff dimension of the random middle third Cantor set." In Proceedings of the ITI 2009 31st International Conference on Information Technology Interfaces (ITI). IEEE, 2009. http://dx.doi.org/10.1109/iti.2009.5196094.

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Aliyev, A., and A. Jalilov. "Computing Hausdorff Dimension of Invariant Measure of Circle Maps." In 2023 3rd International Conference on Technological Advancements in Computational Sciences (ICTACS). IEEE, 2023. http://dx.doi.org/10.1109/ictacs59847.2023.10390237.

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ŽUBRINIĆ, DARKO. "HAUSDORFF DIMENSION OF SINGULAR SETS OF SOBOLEV FUNCTIONS AND APPLICATIONS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0076.

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Mohapatra, Subrajeet, and Dipti Patra. "Automated leukemia detection using hausdorff dimension in blood microscopic images." In 2010 International Conference on Emerging Trends in Robotics and Communication Technologies (INTERACT 2010). IEEE, 2010. http://dx.doi.org/10.1109/interact.2010.5706196.

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Biswas, Biswajit, Abhishek Dey, and Kashi Nath Dey. "Remote sensing image fusion using Hausdorff fractal dimension in shearlet domain." In 2015 International Conference on Advances in Computing, Communications and Informatics (ICACCI). IEEE, 2015. http://dx.doi.org/10.1109/icacci.2015.7275939.

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Steffi Vanthana, P., and A. Muthukumar. "Iris authentication using Gray Level Co-occurrence Matrix and Hausdorff Dimension." In 2015 International Conference on Computer Communication and Informatics (ICCCI). IEEE, 2015. http://dx.doi.org/10.1109/iccci.2015.7218133.

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Gui, Yongxin. "Hausdorff Dimension Spectrum of Self-Affine Carpets Indexed by Nonlinear Fibre-Coding." In 2009 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2009. http://dx.doi.org/10.1109/iwcfta.2009.86.

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Imai, Hiroyuki, Masahiro Kumabe, Kenshi Miyabe, Yuki Mizusawa, and Toshio Suzuki. "Rational Sequences Converging to Left-c.e. Reals of Positive Effective Hausdorff Dimension." In The 9th International Conference on Computability Theory and Foundations of Mathematics. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811259296_0005.

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