Banach spaces for piecewise cone hyperbolic maps

Viviane Baladi (1) , Sébastien Gouëzel (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 the complexity is subexponential, our bound implies a spectral gap for the transfer operator corresponding to the physical measures in many cases (for example if $T$ preserves volume, or if the stable dimension is equal to $1$ and the unstable dimension is not zero).

Domaines: Systèmes dynamiques [math.DS]

Viviane Baladi, Sébastien Gouëzel. Banach spaces for piecewise cone hyperbolic maps. Journal of modern dynamics, 2010, 4 (1), pp.91-137. ⟨hal-00402850v2⟩