拓撲熵、全變差與單峰函數

Abstract

摘 要 這份論文所要討論的目的有兩個。第一個，我們將對陳鞏教授和其學生黃庭偉所發表的論文□的一些結果作些微的修改。第二個，我們將證明對分段單調的單峰函數而言，若此函數滿足在初值條件是靈敏的或者滿足H1這個條件的話，那麼將會導致其拓撲熵是正的。

The purpose of the thesis is two-fold. First, we give slight modifications of some of the results in a paper by Chen and Huang \cite{Chen}. Second, we prove that for a piecewise monotone unimodal map, sensitivity on initial conditions or $\mathcal{H}_{1}$ condition implies that the topological entropy of $f$ is positive.