Banach spaces for piecewise cone hyperbolic maps

Viviane Baladi (1) , Sebastien Gouezel (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 IRMAR - Institut de Recherche Mathématique de Rennes

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]

Viviane Baladi, Sebastien Gouezel. Banach spaces for piecewise cone hyperbolic maps. 2009. ⟨hal-00402850v1⟩