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تسجيل مستخدم جديدPositive Lyapunov exponents for cocycles over time one anosov maps
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تأليف
Mauricio Poletti
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We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.
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اقرأ أيضاً
Criteria for the simplicity of the Lyapunov spectra of linear cocycles have been found by Furstenberg, Guivarch-Raugi, Goldsheid-Margulis and, more recently, Bonatti-Viana and Avila-Viana. In all the cases, the authors consider cocycles over hyperbol
ic systems, such as shift maps or Axiom A diffeomorphisms. In this paper we propose to extend such criteria to situations where the base map is just partially hyperbolic. This raises several new issues concerning, among others, the recurrence of the holonomy maps and the (lack of) continuity of the Rokhlin disintegrations of $u$-states. Our main results are stated for certain partially hyperbolic skew-products whose iterates have bounded derivatives along center leaves. They allow us, in particular, to exhibit non-trivial examples of stable simplicity in the partially hyperbolic setting.
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