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Bounded distortion and dimension for non-conformal repellers

Published online by Cambridge University Press:  24 October 2008

K. J. Falconer
K. J. Falconer
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS*
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Abstract

We obtain an expression for the dimension of a mixing repeller of a non-conformal mapping analogous to the well-known Bowen-Ruelle formula for conformal repellers. The dimension is given in terms of a generalized pressure defined in the context of the thermodynamic formalism. In the course of the paper we develop a subadditive version of the thermodynamic formalism that is suited to our needs and also obtain a ‘bounded distortion’ principle applicable to the non-conformal situation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 2 , March 1994 , pp. 315 - 334
Copyright
Copyright © Cambridge Philosophical Society 1994

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