arXiv:2102.08448 Abstract | arXiv Analytics

arXiv:2102.08448 [math.DS]Abstract References Reviews Resources

Simplicity of Lyapunov spectrum for geodesic flows in negative curvature

Published 2021-02-16Version 1

We study the Lyapunov spectrum of the geodesic flow of negatively curved 1/4-pinched Riemannian manifolds. We show that the space of metrics with simple Lyapunov spectrum with respect to the equilibrium state of any H\"older continuous potential is $C^k$ open and dense. The proof relies on a symbolic coding of the flow to apply the simplicity criterion of Avila and Viana in [AV07] and on perturbational results for $k$-jets of geodesic flows established in [KT72].

Comments: 32 pages, 1 figure; comments welcome

Categories: math.DS, math.DG

Subjects: 37J39

Keywords: geodesic flow, negative curvature, simple lyapunov spectrum, riemannian manifolds, equilibrium state

Related articles: Most relevant | Search more

arXiv:1505.05178 [math.DS] (Published 2015-05-19)

On the Lagrange and Markov Dynamical Spectra for Geodesic Flows in Surfaces with Negative Curvature

Sergio Augusto Romaña Ibarra, Carlos Gustavo T. de A. Moreira

arXiv:0707.0666 [math.DS] (Published 2007-07-04, updated 2010-06-30)

Characterization of geodesic flows on T^2 with and without positive topological entropy

Eva Glasmachers, Gerhard Knieper

arXiv:1812.04409 [math.DS] (Published 2018-12-11)