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疊代函數系統中碎形幾何及條件熵的現象和關聯性

By 鄭文巧

Abstract

[[abstract]]預計將研讀熵和維度進一步論文, 更深入研究具有微分方程疊代系統的軌跡函數之entropy 架構. 例如, 在機率空間和緊緻距離拓樸群空間, 兩者都有不同的entropy 定義和結構, 計劃探究尋找彼此性質和關係. 也計劃擴展 measure-theoretic entropy 定義至topological pre-image pressure,尋找變數法則. 對於這些相異的entropy-like 不變之量, 在以Shannon- McMillan- Breimann 定理為動機, 也將探求條件訊息函數的功能和收歛性. 為了將傳統碎形幾何方法延伸到正向對映微分方程系統的實務應用之中, 本計劃將詳細研讀維度方法基本分析, 預測軌跡系統維度基本性質之分析研究. 我們舉了很多動力系統的應用實例, 例如: 研究不變集合dimension 之測度方法與應用. 在這研究中, 我們並比較此一微分方程系統分析模式在測量碎形幾何過程與傳統測度的優異性. 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. During this project, I plan to study entropy and dimension paper, such as ”Solving differential equations by a maximum entropy” and “Hausdorff dimensions of zero‐entropy sets of dynamical systems with positive entropy“. The structure of fractal geometry and the variation of conditional entropy will be discussed for the orbit in some differential equation systems. Then, I plan extend those propositions to topological pressure case. Under the motivation of Shannon‐McMillan‐Breimann theory, how to predict the entropy of the orbits will be researched. The calculation of local dimension and generator are also discussed

Year: 2009
OAI identifier: oai:http://ir.lib.pccu.edu.tw/:987654321/2151
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