Dimension of Scrambled Sets and The Dynamics of Tridiagonal Competitive-Cooperative System

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Title: Dimension of Scrambled Sets and The Dynamics of Tridiagonal Competitive-Cooperative System
Author: Fang, Chun
Contributor organization: University of Helsinki, Faculty of Science, Department of Mathematics and Statistics
Helsingin yliopisto, matemaattis-luonnontieteellinen tiedekunta, matematiikan ja tilastotieteen laitos
Helsingfors universitet, matematisk-naturvetenskapliga fakulteten, institutionen för matematik och statistik
Publisher: Helsingin yliopisto
Date: 2013-10-08
Language: eng
URI: http://urn.fi/URN:ISBN:978-952-10-9298-5
Thesis level: Doctoral dissertation (article-based)
Abstract: One of the central problems in dynamical systems and differential equations is the analysis of the structures of invariant sets. The structures of the invariant sets of a dynamical system or differential equation reflect the complexity of the system or the equation. For example, any omega-limit set of a finite dimensional differential equation is a singleton implies that each bounded solution of the equation eventually stabilizes at some equilibrium state. In general, a dynamical system or differential equation can have very complicated invariant sets or so called chaotic sets. It is of great importance to classify those systems whose minimal invariant sets have certain simple structures and to characterize the complexity of chaotic type sets in general dynamical systems. In this thesis, we focus on the following two important problems: estimates for the dimension of chaotic sets and stable sets in a finite positive entropy system, and characterizations of minimal sets of nonautonomous tridiagonal competitive-cooperative systems.
Subject: mathematics
Rights: Julkaisu on tekijänoikeussäännösten alainen. Teosta voi lukea ja tulostaa henkilökohtaista käyttöä varten. Käyttö kaupallisiin tarkoituksiin on kielletty.

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