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

Renato Feres, Anatoly Katok

Research output: Contribution to journalArticle

19 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)427-432
Number of pages6
JournalErgodic Theory and Dynamical Systems
Volume9
Issue number3
DOIs
StatePublished - Jan 1 1989

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Geodesic Flow
Rigidity
Lyapunov Exponent
Tensors
Dynamical systems
Tensor
Dynamical system
Affine Connection
Invariant
Negative Curvature
Riemannian Manifold

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. / Feres, Renato; Katok, Anatoly.

In: Ergodic Theory and Dynamical Systems, Vol. 9, No. 3, 01.01.1989, p. 427-432.

Research output: Contribution to journalArticle

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