On essential coexistence of zero and nonzero Lyapunov exponents

Jianyu Chen

doi:10.3934/dcds.2012.32.4149

Article Contents

2012, Volume 32, Issue 12: 4149-4170. Doi: 10.3934/dcds.2012.32.4149

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On essential coexistence of zero and nonzero Lyapunov exponents

Jianyu Chen^1,

1.
Department of Mathematics, Pennsylvania State University, University Park, PA 16802

Received: February 28, 2011

Revised: April 30, 2012

Published: November 2012

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Abstract

We show that there exists a $C^\infty$ volume preserving diffeomorphism $P$ of a compact smooth Riemannian manifold $\mathcal{M}$ of dimension 4, which is close to the identity map and has nonzero Lyapunov exponents on an open and dense subset $\mathcal{G}$ of not full measure and has zero Lyapunov exponent on the complement of $\mathcal{G}$. Moreover, $P|\mathcal{G}$ has countably many disjoint open ergodic components.

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Mathematics Subject Classification: 37D25, 37D30.

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