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Dynamical upper bounds for Hausdorff dimension ofinvariant sets

Published online by Cambridge University Press:  01 June 1997

YINGJIE ZHANG
YINGJIE ZHANG
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA (e-mail: yzhang@math.msu.edu)
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Abstract

We study the Hausdorff dimension of invariant sets for expanding maps and that of hyperbolic sets on unstable manifolds. Upper bounds for the Hausdorff dimension are given in terms of topological pressure, or topological entropy and Lyapunov exponents.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 3 , June 1997 , pp. 739 - 756
Copyright
1997 Cambridge University Press

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