# American Institute of Mathematical Sciences

January  2019, 39(1): 521-551. doi: 10.3934/dcds.2019022

## Non-hyperbolic behavior of geodesic flows of rank 1 surfaces

 Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária - Ilha do Fundão, Av. Athos da Silveira Ramos 149, Rio de Janeiro 21945-909, Brazil

KG has been supported by CNPq (Brazil). She is very grateful for the comments by the referee

Received  April 2018 Revised  July 2018 Published  October 2018

We prove that for the geodesic flow of a rank 1 Riemannian surface which is expansive but not Anosov the Hausdorff dimension of the set of vectors with only zero Lyapunov exponents is large.

Citation: Katrin Gelfert. Non-hyperbolic behavior of geodesic flows of rank 1 surfaces. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 521-551. doi: 10.3934/dcds.2019022
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##### References:
local product structure
Parametrization $R = R_v$ of the local cross section in a neighborhood of a vector $v$. Here $\pi$ denotes the projection of the centre stable leaf onto the cross section given by the local product structure.
Schematic construction of $\nu$: $m_\ell$-cylinders which intersect $\Sigma^\ell$ (bold), cylinders on which $\nu$ is distributed (bold blue), $\ell = 1,2,3$
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