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Contributions to the geometric and ergodic theory of conservative flows

  • MÁRIO BESSA (a1) and JORGE ROCHA (a2)

Abstract

We prove the following dichotomy for vector fields in a $C^1$ -residual subset of volume-preserving flows: for Lebesgue-almost every point, either all of its Lyapunov exponents are equal to zero or its orbit has a dominated splitting. Moreover, we prove that a volume-preserving and $C^1$ -stably ergodic flow can be $C^1$ -approximated by another volume-preserving flow which is non-uniformly hyperbolic.

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Contributions to the geometric and ergodic theory of conservative flows

  • MÁRIO BESSA (a1) and JORGE ROCHA (a2)

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