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The Almost Periodicity、Chaotic Property and Topological Ergodicity

Author: XingXiuYing
Tutor: WangLiDong
School: Liaoning Normal University
Course: Basic mathematics
Keywords: distributional chaos in a sequence distributional chaos Ruelle-Takens chaos Xiong chaos Kato chaos almost periodic point topological transitivity sensitivity topologically ergodic topologically doubly ergodic
CLC: O415.5
Type: Master's thesis
Year: 2009
Downloads: 28
Quote: 1
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Abstract


Content: The system induced by the continuous self-map of the compact metric space is called the dynamic system or the compact system, and research of chaos become the branch that can’t ignore in the field of dynamical system. Now chaos has been one of the main research subjects concerned by scientists in all fields. In this paper we mainly discuss the chaotic properties on the general compact space、symbolic space and Banach space, then reach some important results as follows:1. In the compact system, distributional chaos in a sequence' dissertation">distributional chaos in a sequence、distributional chaos and Ruelle-Takens chaos are non-equivalent to each other.2. By constructing a minimal sub-shift, we prove that there exists a minimal setΛ(?)Σsuch thatσΛis topologically ergodic, topologically doubly ergodic and Xiong-chaotic.3. We discuss the property of chaos for Banach space, it is obtained that there exists a compact sub-setΛ?A( f) such that fΛis Xiong-chaotic and Kato chaotic.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Nonlinear physics > Chaos Theory
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