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Bowen’s equation in the non-uniform setting

Published online by Cambridge University Press:  20 July 2010

VAUGHN CLIMENHAGA*
Affiliation:
Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802, USA (email: climenha@math.psu.edu)

Abstract

We show that Bowen’s equation, which characterizes the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered contraction condition. Among other things, this allows us to compute the dimension spectrum for Lyapunov exponents for maps with parabolic periodic points, and to relate the Hausdorff dimension to the topological entropy for arbitrary subsets of symbolic space with the appropriate metric.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2010

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