Stability versus chaos for a partial differential equation
type: Item
instance of: scholarly article
title: Stability versus chaos for a partial differential equation
zbMATH Open document ID: 1005.35029
DOI: 10.1016/S0960-0779(01)00190-4
author: Józef Myjak
author: Ryszard Rudnicki
published in: Chaos, Solitons and Fractals
publication date: 2002-08-19T00:00:00Z
review text: The main purposes of the presented paper is to investigate a semiflow generated by a first-order partial differential equation, to show that stability and chaos depend on the proper choice of the phase space and to develop a method in order to construct an invariant measure under the semiflow \(\{S_t\}_{t\geq 0}\). The paper is organized as follows. The introduction contains several assumptions and preliminary remarks and is followed by Section 2, ``Main results''. Section 3, ``Invariant measure'' developes the construction of an invariant measure under the shift semiflow \(\{S_t\}\). Clear and accurate, this study opens new ways for studying the stability of chaotic systems.
Mathematics Subject Classification ID: 35F15
Mathematics Subject Classification ID: 37L40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 37L15
zbMATH DE Number: 1783809
zbMATH Keywords: ergodic and analytic properties
zbMATH Keywords: choice of the phase
zbMATH Keywords: invariant measure
Wikidata QID: Q115337377
MaRDI profile type: Publication
cites work: Interval maps, factors of maps, and chaos
cites work: Stationary functions and their applications to the theory of turbulence. I: Stationary functions
cites work: Ergodicity and exactness of the shift on C[0,\(\infty)\) and the semiflow of a first-order partial differential equation
cites work: Hypercyclic and chaotic semigroups of linear operators
cites work: Invariant measures and a linear model of turbulence
cites work: Turbulent solutions of a first order partial differential equation
cites work: Invariant measures for the flow of a first order partial differential equation
cites work: Strong ergodic properties of a first-order partial differential equation
cites work: Q4846980
cites work: Q4870975
full work available at URL: s0960-0779(01)00190-4
OpenAlex ID: W1997233737
description: scientific article; zbMATH DE number 1783809