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

Mauricio Poletti

doi:10.3934/dcds.2018228

Article Contents

2018, Volume 38, Issue 10: 5163-5188. Doi: 10.3934/dcds.2018228

This issue Previous Article Existence and non-existence results for variational higher order elliptic systems Next Article A quantitative shrinking target result on Sturmian sequences for rotations

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

Mauricio Poletti

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

Received: December 31, 2017

Published: September 2018

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Abstract

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.

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

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

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

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

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Figure 4. perturbation of $H$

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