半群函數下局部熵與碎型維度之結構

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Title:	半群函數下局部熵與碎型維度之結構 The Structure of Local Entropy and Fractal Dimension under Semigroup Action
Authors:	鄭文巧
Contributors:	應用數學系
Date:	2016
Issue Date:	2019-11-08 09:43:45 (UTC+8)
Abstract:	局部拓撲熵是熱力學公式研究中一個重要的不變數，在遍歷理論、動力系統理論、維數理論和重分形理論的研究中發揮著極其重要的作用，它的研究一直是動力系統中極受關注的領域之一。在這研究中，我們並比較此一系統分析模式在測量碎形幾何過程與傳統測度的優異性.本計劃將探討複雜性半群系統之已知的碎形產生方法，應用測度熵平均數，並討論很多相關之性質.同時，針對條件熵參數與碎形之估計量，我們提出適當可行估計法的評判準則，例如，generator原創存在的工作與 local dimension計算方法.期望有進一步成果. I have been interested in Dynamical Systems—entropy theory since obtaining Ph.d degree under the direction of Professor Sheldon Newhouse at Michigan State University. In Taiwan, I devoted most of my time to investigate relationships among different types of entropy-like and pressure-like invariants. Then I and my partners give different proofs of the variational principle with more advanced ergodic techniques. Those properties can describe the structure of local uncertainty. Moreover, the notion of local entropy dimension was introduced to measure the complexity of zero entropy dynamical systems in 2013. I plan to calculate the local entropy dimension from some examples with my partners. Then we give the formulas of calculating the local entropy and dimension of the piecewise monotone map and sub-shift of symbolic dynamics. We also construct some examples to show that e^e^^y number in (0,1) can be attained by the entropy dimensions of the dynamical systems and a dynamical system whose entropy dimension is one and topological entropy is zero. We also predict the other indicates that the l^^wer and upper entropy dimensions and that in the seme of Bowen can be different.
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