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Discrete Lyapunov exponents and Hausdorff dimension

Published online by Cambridge University Press:  01 February 2000

SHMUEL FRIEDLAND
SHMUEL FRIEDLAND
Affiliation:
The University of Illinois at Chicago, Department of Mathematics, Statistics and Computer Science, 851 S. Morgan Street, Chicago, Illinois 60607-7045, USA (e-mail: friedlan@uic.edu)
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Abstract

We study certain metrics on subshifts of finite type for which we define the discrete analogs of Lyapunov exponents. We prove Young's formula for $\mu$-Hausdorff dimension. We give sufficient conditions on the above metrics for which the Hausdorff dimension is given by thermodynamic formalism. We apply these results to the Hausdorff dimension of the limit sets of geometrically finite, purely loxodromic, Kleinian groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 1 , February 2000 , pp. 145 - 172
Copyright
2000 Cambridge University Press

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