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$C^1$-openness of non-uniform hyperbolic diffeomorphisms with bounded $C^2$ norm

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arxiv 1808.04003 v2 pith:E5357CZS submitted 2018-08-12 math.DS

Chao Liang , Karina Marin , Jiagang Yang This is my paper · ORCID
classification math.DS
keywords hyperbolicnon-uniformboundeddiffeomorphismssubsetcentercertainclass
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abstract

We study the $C^1$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^2$ partially hyperbolic symplectic systems which have bounded $C^2$ distance to the identity. In this set, we prove the stability of non-uniform hyperbolicity as a function of the diffeomorphism and the measure, and the existence of an open and dense subset of continuity points for the center Lyapunov exponents. These results are generalized to the volume-preserving context.

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