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2010•Dalian Minzu Xueyuan xuebaoRequires access

Chaos and Topological Semi-conjugacy

Yang Yu-e

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Abstract

Let(X,f),(Y,g)be topological dynamical systems,where f and g are topologically semi-conjugate.This paper presents chaoticity as an extension that is based on special properties of topological semi-conjugacy.As an application,it gives a new proof for the fact that the topological entropy of interval maps being greater than 0 is equivalent to a set of almost periodic points containing an uncountable chaotic set.

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What this paper is about

Let(X,f),(Y,g)be topological dynamical systems,where f and g are topologically semi-conjugate.This paper presents chaoticity as an extension that is based on special properties of topological semi-conjugacy.As an application,it gives a new proof for the fact that the topological entropy of interval maps being greater than 0 is equivalent to a set of almost periodic points containing an uncountable chaotic set.

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Available abstract

Let(X,f),(Y,g)be topological dynamical systems,where f and g are topologically semi-conjugate.This paper presents chaoticity as an extension that is based on special properties of topological semi-conjugacy.As an application,it gives a new proof for the fact that the topological entropy of interval maps being greater than 0 is equivalent to a set of almost periodic points containing an uncountable chaotic set.

Key concepts: Uncountable set, Topological entropy, Topological conjugacy, Mathematics, Conjugacy class, Extension (predicate logic), Interval (graph theory), Dynamical systems theory

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