Chaotic Properties of Mappings on a Probability Space

Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. We first give sufficient conditions (both topological and ergodic) on an endomorphism to ensure the sensitivity property. Then, a strong sensitivity concept is introduced. Sufficient conditions on a t...

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Veröffentlicht in:	Journal of mathematical analysis and applications 2002-02, Vol.266 (2), p.420-431
Hauptverfasser:	Abraham, Christophe, Biau, Gérard, Cadre, Benoı̂t
Format:	Artikel
Sprache:	eng
Schlagworte:	chaos endomorphism exact Exact sciences and technology initial conditions Mathematics mixing Sciences and techniques of general use sensitive dependence
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. We first give sufficient conditions (both topological and ergodic) on an endomorphism to ensure the sensitivity property. Then, a strong sensitivity concept is introduced. Sufficient conditions on a transformation implying strong sensitivity are given. We also provide bounds for the strong sensitivity constant.
ISSN:	0022-247X 1096-0813
DOI:	10.1006/jmaa.2001.7754