Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Lyapunov spectrum for geodesic flows of rank 1 surfaces

Pages: 1841 - 1872, Volume 34, Issue 5, May 2014      doi:10.3934/dcds.2014.34.1841

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Keith Burns - Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, United States (email)
Katrin Gelfert - Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária - Ilha do Fundão, Rio de Janeiro 21945-909, Brazil (email)

Abstract: We give estimates on the Hausdorff dimension of the levels sets of the Lyapunov exponent for the geodesic flow of a compact rank 1 surface. We show that the level sets of points with small (but non-zero) exponents has full Hausdorff dimension, but carries small topological entropy.

Keywords:  Lyapunov exponents, multifractal formalism, Hausdorff dimension, entropy, geodesic flow, rank 1 surfaces, pressure, shadowing.
Mathematics Subject Classification:  Primary: 37D25, 37D35, 28D20, 37C45.

Received: May 2012;      Revised: August 2013;      Available Online: October 2013.