Devaney's chaos or 2-scattering implies Li–Yorke's chaos

By Wen Huang, Xiangdong Ye. 2002

296 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/131bfa14f121295ca63f50bfed7a0fef4ddeb213

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Li-Yorke chaos in the system with impacts (2009, background): “While the existence of periodic solutions, as it was discovered later, is a particular case of Sharkovsky’s theorem [26], the scrambled set remains the feature, which distinguishes Li–Yorke chaos from other definitions [6,13].”
Chaos of time-varying discrete dynamical systems (2009, background): “It is known that they are not equivalent in general [10,18].”
Asymptotic pairs in positive-entropy systems (2002, result): “The set of asymptotic pairs of any topological dynamical system has been shown to be first category in [14]: it is a small set, but not too small according to the present result.”
Discrete chaos in Banach spaces (2005, background): “Let V be a subset of a metric space (X, d). A continuous map f : V → V is said to be chaotic on V in the sense of Devaney if f satisfies Properties (1) and (2) on V . In this paper, chaos of system (1.1) is always defined in the sense of Devaney, which may be on a space X or on a subset V ⊂ X. Recen”
On shadowing: Ordinary and ergodic (2010, background): “Topological mixing and specification are two another formal ways to get some special dynamical properties and also chaos in global sense [2,11].”
Recent development of chaos theory in topological dynamics (2015, background): “6 ([46]) Let (X,T ) be a non-periodic transitive system.”
Mean equicontinuity and mean sensitivity (2013, background): “Assume that P(X, T ) is dense in X × X, for example (X, T ) is weakly mixing or transitive with a fixed point [20].”
Local entropy theory (2009, background): “Following the ideas and methods developed by Rosenthal [89], Glasner–Weiss [40], and Huang–Ye [57], Kerr and Li, in their recent work [74], introduced various notions of independence.”