Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle

Liang, Chao; Marin, Karina; Yang, Jiagang

doi:10.1016/j.anihpc.2018.01.007

Liang, Chao ; Marin, Karina ; Yang, Jiagang

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1687-1706.

Résumé

We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps are $C^{r}$ open and there exists a $C^{r}$ open and dense subset of continuity points for the center Lyapunov exponents. We also generalize these results to volume-preserving systems.

MR Zbl

DOI : 10.1016/j.anihpc.2018.01.007

Classification : 37D25, 37D30
Mots clés : Partially hyperbolic diffeomorphisms, Lyapunov exponents, Non-uniform hyperbolicity

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     author = {Liang, Chao and Marin, Karina and Yang, Jiagang},
     title = {Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1687--1706},
     publisher = {Elsevier},
     volume = {35},
     number = {6},
     year = {2018},
     doi = {10.1016/j.anihpc.2018.01.007},
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     zbl = {1398.37025},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.007/}
}

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Liang, Chao; Marin, Karina; Yang, Jiagang. Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 6, pp. 1687-1706. doi : 10.1016/j.anihpc.2018.01.007. http://www.numdam.org/articles/10.1016/j.anihpc.2018.01.007/

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