# American Institute of Mathematical Sciences

October  2018, 38(10): 5163-5188. doi: 10.3934/dcds.2018228

## Stably positive Lyapunov exponents for symplectic linear cocycles over partially hyperbolic diffeomorphisms

 LAGA - Université Paris 13, 99 Av. Jean-Baptiste Clément, 93430 Villetaneus, France

Received  January 2018 Published  July 2018

We consider $\mathit{Sp}\left( 2\mathit{d},\mathbb{R} \right)$ cocycles over two classes of partially hyperbolic diffeomorphisms: having compact center leaves and time one maps of Anosov flows. We prove that the Lyapunov exponents are non-zero in an open and dense set in the Hölder topology.

Citation: Mauricio Poletti. Stably positive Lyapunov exponents for symplectic linear cocycles over partially hyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5163-5188. doi: 10.3934/dcds.2018228
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##### References:
definition of $z_n$ and $x'$
definition $h:\mathcal{W}^c(p)\to \mathcal{W}^c(p)$ for class ${\bf{A}}$
definition $h:\mathcal{W}^c(p)\to \mathcal{W}^c(p)$ for class ${\bf{B}}$
perturbation of $H$
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