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Common extensions and hyperbolic factor maps for coded systems

Published online by Cambridge University Press:  19 September 2008

Doris Fiebig
Doris Fiebig
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
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Abstract

The classification of dynamical systems by the existence of certain common extensions has been carried out very successfully in the class of shifts of finite type (‘finite equivalence’, ‘almost topological conjugacy‘). We consider generalizations of these notions in the class of coded systems. Topological entropy is shown to be a complete invariant for the existence of a common coded entropy preserving extension. In contrast to the shift of finite type setting, this extension cannot be made bounded-to-1 in general. Common extensions with hyperbolic factor maps lead to a version of almost topological conjugacy for coded systems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 3 , June 1995 , pp. 517 - 534
Copyright
Copyright © Cambridge University Press 1995

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