We study the Ruelle and Selberg zeta functions for C r Anosov flows, r> 2, on a compact
smooth manifold. We prove several results, the most remarkable being (a) for C∞ flows the …

By introducing appropriate Banach spaces one can study the spectral properties of the
generator of the semigroup defined by an Anosov flow. Consequently, it is possible to easily …

On July 9, 2001, Springer invited me to contribute a monograph on dynamical systems. I
immediately accepted, offering to write a book on dynamical zeta functions and dynamical …

We prove exponential decay of correlations for the billiard flow associated with a two-
dimensional finite horizon Lorentz Gas (ie, the Sinai billiard flow with finite horizon). Along …

Compact locally maximal hyperbolic sets are studied via geometrically defined functional
spaces that take advantage of the smoothness of the map in a neighborhood of the …

For any C r contact Anosov flow with r⩾ 3, we construct a scale of Hilbert spaces, which are
embedded in the space of distributions on the phase space and contain all the C r functions …

We consider the semi-classical (or Gutzwiller–Voros) zeta functions for C^ ∞ C∞ contact
Anosov flows. Analyzing the spectra of the generators of some transfer operators associated …

We study the twisted Ruelle zeta function ζ _X (s) ζ X (s) for smooth Anosov vector fields X
acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove the …

We define the prequantization of a symplectic Anosov diffeomorphism f: M-> M, which is a U
(1) extension of the diffeomorphism f preserving an associated specific connection, and …

We present a new scale U^ t, s _p U pt, s (s<-t< 0 s<-t< 0 and 1 ≤ p< ∞ 1≤ p<∞) of
anisotropic Banach spaces, defined via Paley–Littlewood, on which the transfer operator L …