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Relevant bibliographies by topics / Sharkovskii's Theorem

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Journal articles

Academic literature on the topic 'Sharkovskii's Theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Sharkovskii's Theorem"

1

ZGLICZYŃSKI, PIOTR. "Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps." Ergodic Theory and Dynamical Systems 19, no. 6 (1999): 1655–84. http://dx.doi.org/10.1017/s0143385799141749.

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We present Sharkovskii's theorem for multidimensional perturbations of one-dimensional maps. We show that if an unperturbed one-dimensional map has a point of period $n$, then sufficiently close multidimensional perturbations of this map have periodic points of all periods which are allowed by Sharkovskii's theorem.

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2

Du, Bau-Sen. "The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem." Bulletin of the Australian Mathematical Society 31, no. 1 (1985): 89–103. http://dx.doi.org/10.1017/s0004972700002306.

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Let f(x) be a continuous function from a compact real interval into itself with a periodic orbit of minimal period m, where m is not an integral power of 2. Then, by Sharkovskii's theorem, for every positive integer n with m → n in the Sharkovskii ordering defined below, a lower bound on the number of periodic orbits of f(x) with minimal period n is 1. Could we improve this lower bound from 1 to some larger number? In this paper, we give a complete answer to this question.

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3

Andres, Jan, Tomáš Fürst, and Karel Pastor. "Sharkovskii's theorem, differential inclusions, and beyond." Topological Methods in Nonlinear Analysis 33, no. 1 (2009): 149. http://dx.doi.org/10.12775/tmna.2009.011.

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4

ANDRES, JAN, PAVLA ŠNYRYCHOVÁ та PIOTR SZUCA. "SHARKOVSKII'S THEOREM FOR CONNECTIVITY Gδ-RELATIONS". International Journal of Bifurcation and Chaos 16, № 08 (2006): 2377–93. http://dx.doi.org/10.1142/s0218127406016136.

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A version of Sharkovskii's cycle coexistence theorem is formulated for a composition of connectivity Gδ-relations with closed values. Thus, a multivalued version in [Andres & Pastor, 2005] holding with at most two exceptions for M-maps, jointly with a single-valued version in [Szuca, 2003], for functions with a connectivity Gδ-graph, are generalized. In particular, our statement is applicable to differential inclusions as well as to some discontinuous functions.

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5

Barton, Reid, and Keith Burns. "A Simple Special Case of Sharkovskii's Theorem." American Mathematical Monthly 107, no. 10 (2000): 932. http://dx.doi.org/10.2307/2695586.

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6

Barton, Reid, and Keith Burns. "A Simple Special Case of Sharkovskii's Theorem." American Mathematical Monthly 107, no. 10 (2000): 932–33. http://dx.doi.org/10.1080/00029890.2000.12005293.

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7

Lee, M. H. "Defining Chaos in the Logistic Map by Sharkovskii's Theorem." Acta Physica Polonica B 44, no. 5 (2013): 925. http://dx.doi.org/10.5506/aphyspolb.44.925.

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8

Du, Bau-Sen, and Ming-Chia Li. "A refinement of Sharkovskii's theorem on orbit types characterized by two parameters." Journal of Mathematical Analysis and Applications 278, no. 1 (2003): 77–82. http://dx.doi.org/10.1016/s0022-247x(02)00513-9.

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9

Ye, Xiangdong. "D-function of a minimal set and an extension of Sharkovskii's theorem to minimal sets." Ergodic Theory and Dynamical Systems 12, no. 2 (1992): 365–76. http://dx.doi.org/10.1017/s0143385700006817.

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AbstractLetXbe a compact Hausdorff space,f∈C0(X, X) andA⊂Xa minimal set off. We first introduce a new topological invariant, the D-function of a minimal set, by the investigation of the decomposition of the minimal set A under the action offn,n∈N. Then important properties about the invariant and the existence of minimal set with a given D-function in some subshift of finite type are discussed. Finally Sharkovskii's theorem is generalized to minimal sets of continuous mappings from the interval into itself.

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10

Du, Bau-Sen. "The minimal number of periodic orbits of periods guaranteed in Sharkovskii's theorem: Corrigendum." Bulletin of the Australian Mathematical Society 32, no. 1 (1985): 159. http://dx.doi.org/10.1017/s0004972700009837.

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