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Rigidity of Lyapunov exponents for geodesic flows

Published on:

8 February 2024

Primary Category:

Dynamical Systems

Paper Authors:

Nestor Nina Zarate,

Sergio Romaña

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Key Details

Proves rigidity of Lyapunov exponents for surfaces without focal points

Extends previous result on rigidity of Lyapunov exponents to Anosov geodesic flows on surfaces

Uses different techniques to extend a rigidity result to finite volume case with maximal/minimal exponents

AI generated summary

Rigidity of Lyapunov exponents for geodesic flows

This paper proves that for a surface without focal points, if the Lyapunov exponents are constant for all periodic orbits, the surface has constant negative curvature or is the flat 2-torus. The same result is shown for Anosov geodesic flows on surfaces, generalizing a previous result in dimension two. The paper also extends a previous finite volume rigidity result to the case where Lyapunov exponents are maximal or minimal along all periodic orbits.

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