A Note on a Misuirewicz's Theorem

In this paper,we improve a Misuirewicz's theorem and give a new proof of small conjecture on topological entropy.

A Note on Topological Entropy of Continuous Self-Maps

Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler＇s topological entropy is also presented.

关于迭序列的子列极限点

本文讨论了度量空间上一个连续自映射击一点处的迭代序列的子列极限点集的结构，所得的结果统一和推广了Ｄｉａｚ和Ｍｅｔｃａｌｆ￣［１］，Ｍａｉｔｉ和Ｂａｂｕ￣［２，４］和Ｐａｒｋ￣［３］的若干结果．

The Monotone Iterative Roots of a Class of Self-Mappings on the Interval

Let I = [0,1], 0 < a < b < 1. Let Φab ≡ {F ∈ C0(I): both F|[0,a] and F|[b, 1] are strictly increasing, and F|[a, b] is constant }. In this paper we discuss necessary and sufficient conditions for F ∈Φab to have monotone iterative roots.