Title: 拓撲熵、全變差與單峰函數Topological Entropy, Total Variation and Unimodal Maps Authors: 張秀禎Hsiu-Chen Chang莊重Dr. Jonq Juang應用數學系所 Keywords: 全變差;拓撲熵;靈敏度;單峰;單峰函數;variation;total variation;topological entropy;sensitivity;sensitive;unimodal;unimodal map Issue Date: 2000 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. URI: http://140.113.39.130/cdrfb3/record/nctu/#NT890507010http://hdl.handle.net/11536/67689 Appears in Collections: Thesis