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Stability of the spectrum for transfer operators
- G. Keller, C. Liverani
- Mathematics
- 1999
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
- C. Liverani, B. Saussol, S. Vaienti
- Mathematics, Computer ScienceErgodic Theory and Dynamical Systems
- 1 June 1999
TLDR
Decay of correlations
- C. Liverani
- Linguistics
- 1 September 1995
*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
- M. Blank, G. Keller, C. Liverani
- Mathematics
- 10 April 2001
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
- S. Gouezel, C. Liverani
- MathematicsErgodic Theory and Dynamical Systems
- 14 May 2004
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
- C. Liverani
- Mathematics
- 1 February 1995
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
- G. Keller, C. Liverani
- Mathematics
- 13 October 2008
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
- C. Liverani
- Mathematics
- 1995
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
- C. Liverani
- Mathematics
- 1 May 2004
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
- P. Giulietti, C. Liverani, M. Pollicott
- Mathematics
- 5 March 2012
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…
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