Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

Renato Feres; Anatoly Katok

doi:10.1017/S0143385700005071

Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

Renato Feres, Anatoly Katok

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.

Original language	English (US)
Pages (from-to)	427-432
Number of pages	6
Journal	Ergodic Theory and Dynamical Systems
Volume	9
Issue number	3
DOIs	https://doi.org/10.1017/S0143385700005071
State	Published - Sep 1989

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows",

abstract = "We consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.",

author = "Renato Feres and Anatoly Katok",

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AB - We consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.

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Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

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