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A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems

Published online by Cambridge University Press:  14 October 2010

Luis M. Barreira
Luis M. Barreira
Affiliation:
Department of Mathematics, The Pennsylvania State UniversityUniversity Park, PA 16802USA (e-mail: luis@math.psu.edu)
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Abstract

A non-additive version of the thermodynamic formalism is developed. This allows us to obtain lower and upper bounds for the dimension of a broad class of Cantor-like sets. These are constructed with a decreasing sequence of closed sets that may satisfy no asymptotic behavior. Moreover, they can be coded by arbitrary symbolic dynamics, and the geometry of the construction may depend on all the symbolic past. Applications include estimates of dimension for hyperbolic sets of maps that need not be differentiable.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 5 , October 1996 , pp. 871 - 927
Copyright
Copyright © Cambridge University Press 1996

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