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

Published online by Cambridge University Press:  19 September 2008

Renato Feres  and
Anatoly Katok
Renato Feres
Affiliation:
Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA
Anatoly Katok
Affiliation:
Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 3 , September 1989 , pp. 427 - 432
Copyright
Copyright © Cambridge University Press 1989

References

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