Banach spaces for piecewise cone hyperbolic maps
Résumé
We consider piecewise cone hyperbolic systems satisfying a bunching condition and we obtain a bound on the essential spectral radius of the associated weighted transfer operators acting on anisotropic Sobolev spaces. The bunching condition is always satisfied in dimension two, and our results give a unifying treatment of the work of Demers-Liverani and our previous work. When hyperbolicity dominates complexity, our bound implies a spectral gap for the transfer operator corresponding to the physical measures.
Domaines
Systèmes dynamiques [math.DS]
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