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Research on the Properties of Hyperspace Induced Dynamic System

Author: LianPan
Tutor: GuoMengShu
School: Harbin Institute of Technology
Course: Basic mathematics
Keywords: discrete dynamic system sensitivity uniquely-ergodic inducedset-valued system
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 17
Quote: 0
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Abstract


Discrete dynamic system is used wildly to describe the model in science, socialscience, engineer technique. Induced hyperspace dynamic system is the system whichis generated by the closed but not empty set of the original system. In the recent tenyears, the relationship between these two kinds system has captured many people’sinterest and obtained fruitful results.This paper is mainly focused on the relationship between discrete dynamicsystems and its induced hyperspace dynamic systems. We generaliz some conclusionson sensitivity. We study sensitivity on the initial conditions,strongly sensitivity,asymptotic sensitivity and Li-Yorke sensitivity of these two kinds of dynamic systems.On the other hand we obtain the result about uniquely-ergodic property.Also we provethe uniquely-ergodic measure is atomic and give the relationship on measure mixingproperty. In the end we give a character of the dynamic system which induced auniquely-ergodic dynamic system.

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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