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Connecting ergodicity and dimension in dynamical systems

Published online by Cambridge University Press:  19 September 2008

C. D. Cutler
C. D. Cutler
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, CanadaN2L 3G1
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Abstract

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In this paper we make precise the relationship between local or pointwise dimension and the dimension structure of Borel probability measures on metric spaces. Sufficient conditions for exact-dimensionality of the stationary ergodic distributions associated with a dynamical system are obtained. A counterexample is provided to show that ergodicity alone is not sufficient to guarantee exactdimensionality even in the case of continuous maps or flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 3 , September 1990 , pp. 451 - 462
Copyright
Copyright © Cambridge University Press 1990

References

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