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The Lyapunov spectrum of some parabolic systems

Published online by Cambridge University Press:  01 June 2009

KATRIN GELFERT  and
MICHAŁ RAMS
KATRIN GELFERT
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, USA (email: gelfert@pks.mpg.de)
MICHAŁ RAMS
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland (email: m.rams@impan.gov.pl)
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Abstract

We study the Hausdorff dimension for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topological entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 3 , June 2009 , pp. 919 - 940
Copyright
Copyright © Cambridge University Press 2008

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