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Stability of the spectrum for transfer operators
We prove stability of the isolated eigenvalues of transfer operators satisfying a Lasota-Yorke type inequality under a broad class of random and nonrandom perturbations including Ulam-type
A probabilistic approach to intermittency
This method essentially gives the optimal polynomial bound for the decay of correlations, the degree depending on the order of the tangency at the neutral fixed point.
Decay of correlations
*Dedicated to Micheline Ishay I would like to thank P. Boyland, L. Chierchia, V. Donnay, G. De Martino, C. Gole, J. L. Lebowitz, M. Lyubich, M. Rychlik, I. G. Schwarz, S. Vaienti and especially G.
Ruelle?Perron?Frobenius spectrum for Anosov maps
We extend a number of results from one-dimensional dynamics based on spectral properties of the Ruelle–Perron–Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows
Banach spaces adapted to Anosov systems
We study the spectral properties of the Ruelle–Perron–Frobenius operator associated to an Anosov map on classes of functions with high smoothness. To this end we construct anisotropic Banach spaces
Decay of correlations for piecewise expanding maps
This paper investigates the decay of correlations in a large class of non-Markov one-dimensional expanding maps. The method employed is a special version of a general approach recently proposed by
Rare Events, Escape Rates and Quasistationarity: Some Exact Formulae
We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging from the metric theory of continuos fractions and the Shannon
Central Limit Theorem for Deterministic Systems
A unified approach to obtaining the central limit theorem for hyperbolic dynamical systems is presented. It builds on previous results for one dimensional maps but it applies to the multidimensional
On contact Anosov flows
Exponential decay of correlations for $\Co^{(4)}$ Contact Anosov flows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic flows in strictly
Anosov flows and dynamical zeta functions
We study the Ruelle and Selberg zeta functions for C r Anosov ows, r > 2, on a compact smooth manifold. We prove several results, the most remarkable being (a) for C 1 ows the zeta function is