# American Institute of Mathematical Sciences

December  2012, 32(12): 4149-4170. doi: 10.3934/dcds.2012.32.4149

## On essential coexistence of zero and nonzero Lyapunov exponents

 1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States

Received  March 2011 Revised  May 2012 Published  August 2012

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.
Citation: Jianyu Chen. On essential coexistence of zero and nonzero Lyapunov exponents. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4149-4170. doi: 10.3934/dcds.2012.32.4149
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