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Hausdorff dimension for horseshoes

Published online by Cambridge University Press:  19 September 2008

Heather McCluskey  and
Anthony Manning
Heather McCluskey
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
Anthony Manning
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
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Abstract

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We shall measure how thick a basic set of a C1 axiom A diffeomorphism of a surface is by the Hausdorff dimension of its intersection with an unstable manifold. This depends continuously on the diffeomorphism. Generically a C2 diffeomorphism has attractors whose Hausdorff dimension is not approximated by the dimension of its ergodic measures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 2 , June 1983 , pp. 251 - 260
Copyright
Copyright © Cambridge University Press 1983

References

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