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

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  • 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.

    Mathematics Subject Classification: Primary: 37H15, 37D30, 37D25.


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  • Figure 1.  definition of $z_n$ and $x'$

    Figure 2.  definition $h:\mathcal{W}^c(p)\to \mathcal{W}^c(p)$ for class ${\bf{A}}$

    Figure 3.  definition $h:\mathcal{W}^c(p)\to \mathcal{W}^c(p)$ for class ${\bf{B}}$

    Figure 4.  perturbation of $H$

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