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Orbit entropy in noninvertible mappings

Part of: Connections with other structures, applications Measure-theoretic ergodic theory

Published online by Cambridge University Press:  09 April 2009

Uhland Burkart
Uhland Burkart
Affiliation:
Fachbereich Mathematik, Universität Marburg, Lahnberge, D-3550 Marburg, Federal Republic of Germany
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Abstract

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Bassed on the intrinsic structure of a selfmapping T: S → S of an arbitrary set S, called the orbit-structure of T, a new entropy is defined. The idea is to use the number of preimages of an element x under the iterates of T to characterize the complexity of the transformation T and their orbit graphs. The fundamental properties of the orbit entropy related to iteration, iterative roots and iteration semigroups are studied. For continuous (differentiable) functions of Rn to Rn, the chaos of Li and Yorke is characterized by means of this entropy, mainly using the method of Straffingraphs.

MSC classification

Secondary: 54H20: Topological dynamics 28D20: Entropy and other invariants
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 1 , February 1986 , pp. 95 - 110
Copyright
Copyright © Australian Mathematical Society 1986

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