Relevant bibliographies by topics / Kupka-Smale and Morse-Smale properties

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Kupka-Smale and Morse-Smale properties'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Kupka-Smale and Morse-Smale properties"

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R. Oliveira, Elismar. "Generic properties of Lagrangians on surfaces: The Kupka-Smale theorem." Discrete & Continuous Dynamical Systems - A 21, no. 2 (2008): 551–69. http://dx.doi.org/10.3934/dcds.2008.21.551.

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Rot, T. O., and R. C. A. M. Vandervorst. "Morse–Conley–Floer homology." Journal of Topology and Analysis 06, no. 03 (2014): 305–38. http://dx.doi.org/10.1142/s1793525314500174.

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The gradient flow of a Morse function on a smooth closed manifold generates, under suitable transversality assumptions, the Morse–Smale–Witten complex. The associated Morse homology is an invariant for the manifold, and equals the singular homology, which yields the classical Morse relations. In this paper we define Morse–Conley–Floer homology, which is an analogous homology theory for isolated invariant sets of smooth, not necessarily gradient-like, flows. We prove invariance properties of the Morse–Conley–Floer homology, and show how it gives rise to the Morse–Conley relations.
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ZHAO, XUEZHI. "Non-singular Smale flows on three-dimensional manifolds and Whitehead torsion." Ergodic Theory and Dynamical Systems 31, no. 1 (2009): 301–15. http://dx.doi.org/10.1017/s0143385709000935.

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AbstractThis paper deals with non-singular Smale flows on oriented 3-manifolds. We shall show a relation between the properties of invariant sets of a Smale flow and a kind of Whitehead torsion of the underlying manifold.
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DEELEY, ROBIN J., D. BRADY KILLOUGH, and MICHAEL F. WHITTAKER. "Functorial properties of Putnam’s homology theory for Smale spaces." Ergodic Theory and Dynamical Systems 36, no. 5 (2015): 1411–40. http://dx.doi.org/10.1017/etds.2014.134.

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We investigate functorial properties of Putnam’s homology theory for Smale spaces. Our analysis shows that the addition of a conjugacy condition is necessary to ensure functoriality. Several examples are discussed that elucidate the need for our additional hypotheses. Our second main result is a natural generalization of Putnam’s Pullback Lemma from shifts of finite type to non-wandering Smale spaces.
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DEELEY, ROBIN J., and KAREN R. STRUNG. "Group actions on Smale space -algebras." Ergodic Theory and Dynamical Systems 40, no. 9 (2019): 2368–98. http://dx.doi.org/10.1017/etds.2019.11.

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Group actions on a Smale space and the actions induced on the $\text{C}^{\ast }$-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on the homoclinic algebra. We then show that for irreducible Smale spaces, the property of finite Rokhlin dimension passes from the induced action on the homoclinic algebra to the induced actions on the stable and unstable $\text{C}^{\ast }$-algebras. In each of these cases, we discuss the preservation of properties (such as finite nuclear dimensi
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Batterson, Steve, and John Smillie. "Smale diffeomorphisms and surface topology." Ergodic Theory and Dynamical Systems 5, no. 4 (1985): 519–29. http://dx.doi.org/10.1017/s0143385700003138.

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AbstractThis paper concerns Smale diffeomorphisms of compact oriented surfaces. Relationships are found between the isotopy class of the map and the dynamics of its basic sets. The form of the dynamical properties involves restrictions on periods and reduced zeta functions.
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Amini, Massoud, Ian F. Putnam, and Sarah Saeidi Gholikandi. "Homology for one-dimensional solenoids." MATHEMATICA SCANDINAVICA 121, no. 2 (2017): 219. http://dx.doi.org/10.7146/math.scand.a-26265.

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Smale spaces are a particular class of hyperbolic topological dynamical systems, defined by David Ruelle. The definition was introduced to give an axiomatic description of the dynamical properties of Smale's Axiom A systems when restricted to a basic set. They include Anosov diffeomeorphisms, shifts of finite type and various solenoids constructed by R. F. Williams. The second author constructed a homology theory for Smale spaces which is based on (and extends) Krieger's dimension group invariant for shifts of finite type. In this paper, we compute this homology for the one-dimensional general
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Pédèches, Laure. "Asymptotic properties of various stochastic Cucker-Smale dynamics." Discrete & Continuous Dynamical Systems - A 38, no. 6 (2018): 2731–62. http://dx.doi.org/10.3934/dcds.2018115.

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Jeanjean, Louis. "On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, № 4 (1999): 787–809. http://dx.doi.org/10.1017/s0308210500013147.

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Using the ‘monotonicity trick’ introduced by Struwe, we derive a generic theorem. It says that for a wide class of functionals, having a mountain-pass (MP) geometry, almost every functional in this class has a bounded Palais-Smale sequence at the MP level. Then we show how the generic theorem can be used to obtain, for a given functional, a special Palais–Smale sequence possessing extra properties that help to ensure its convergence. Subsequently, these abstract results are applied to prove the existence of a positive solution for a problem of the formWe assume that the functional associated t
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Pankov, Alexander. "Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems." Advances in Nonlinear Analysis 8, no. 1 (2017): 372–85. http://dx.doi.org/10.1515/anona-2017-0041.

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Abstract Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case. The proof relies on a careful analysis of the energy functional restricted to the generalized Nehari manifold, and the existence and fine properties of special Palais–Smale sequences.
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Dissertations / Theses on the topic "Kupka-Smale and Morse-Smale properties"

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Percie, du Sert Maxime. "Résultats de généricité pour des réseaux." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112130/document.

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Un réseau de cellules est un graphe orienté dont chaque sommet (aussi appelé cellule) représente un ensemble de variables et dont les arcs symbolisent les interactions entre ces variables. Les réseaux de cellules jouent un rôle important dans la modélisation de phénomènes neurologiques, de systèmes économiques ou biologiques, etc.. Soit G un graphe orienté possédant N sommets, on dit qu'une application f=(f_1,...,f_N) de X=X_1×...×X_N dans X (où X_j=R^dj) est admissible, si pour tout sommet j, f_j(x) dépend de x_i seulement si i->j est un arc de G. Dans cette thèse nous montrons que si G es
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Allemand, Giorgis Leo. "Visualisation de champs scalaires guidée par la topologie." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM091/document.

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Les points critiques d’une fonction scalaire (minima, points col et maxima) sont des caractéristiques importantes permettant de décrire de gros ensembles de données, comme par exemple les données topographiques. L’acquisition de ces données introduit souvent du bruit sur les valeurs. Un grand nombre de points critiques sont créés par le bruit, il est donc important de supprimer ces points critiques pour faire une bonne analyse de ces données. Le complexe de Morse-Smale est un objet mathématique qui est étudié dans le domaine de la Visualisation Scientifique car il permet de simplifier des fonc
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Book chapters on the topic "Kupka-Smale and Morse-Smale properties"

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Grines, Viacheslav Z., Timur V. Medvedev, and Olga V. Pochinka. "General Properties of the Morse–Smale Diffeomorphisms." In Developments in Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44847-3_2.

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Čencova, N. N. "Statistical Properties of Smooth Smale Horseshoes." In Mathematics and Its Applications. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4592-0_5.

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Makowsky, J. A., and K. Meer. "On the Complexity of Combinatorial and Metafinite Generating Functions of Graph Properties in the Computational Model of Blum, Shub and Smale." In Computer Science Logic. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44622-2_27.

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Vadim, Kaloshin, and Zhang Ke. "Generic properties of mechanical systems on the two-torus." In Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.003.0013.

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This chapter focuses on proving generic properties of the minimizing orbits of the slow mechanical system. It first proves Theorem 4.5 concerning non-critical but bounded energy, before proving Proposition 4.6 concerning the very high energy. The chapter then proves Proposition 4.7 concerning the critical energy. The proof of Theorem 4.5 consists of three steps. The first proves a Kupka-Smale-like theorem about non-degeneracy of periodic orbits. The second shows that a non-degenerate locally minimal orbit is always hyperbolic. The third finishes the proof by proving the finite local families obtained from the second step are “in general position,” and therefore there are at most two global minimizers for each energy.
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Conference papers on the topic "Kupka-Smale and Morse-Smale properties"

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Zhang, Wei, Ming-Hui Yao, and Dong-Xing Cao. "Shilnikov Type Multi-Pulse Orbits of Functionally Graded Materials Rectangular Plate." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29206.

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Multi-pulse chaotic dynamics of a simply supported functionally graded materials (FGMs) rectangular plate is investigated in this paper. The FGMs rectangular plate is subjected to the transversal and in-plane excitations. The properties of material are graded in the direction of thickness. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the FGMs plate are derived by using the Hamilton’s principle. The four-dimensional averaged equation under the case of 1:2 internal resonance, primary parametric resonance and 1/2-subharmonic resonanc
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