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 of distributions on which the transfer operator has a large spectral gap. In the $\Co^\infty$ case, the spectral radius is arbitrarily small, which yields a description of the correlations with arbitrary precision. Moreover, we obtain sharp spectral stability results for deterministic and random perturbations. In particular, we obtain differentiability results for spectral data (which imply differentiability of the SRB measure, the variance for the CLT, the rates of decay for smooth observable, etc.).

Liverani, C., Gouezel, S. (2006). Banach spaces adapted to Anosov systems. ERGODIC THEORY & DYNAMICAL SYSTEMS, 26(1), 189-217 [10.1017/S0143385705000374].

### Banach spaces adapted to Anosov systems

#### Abstract

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 of distributions on which the transfer operator has a large spectral gap. In the $\Co^\infty$ case, the spectral radius is arbitrarily small, which yields a description of the correlations with arbitrary precision. Moreover, we obtain sharp spectral stability results for deterministic and random perturbations. In particular, we obtain differentiability results for spectral data (which imply differentiability of the SRB measure, the variance for the CLT, the rates of decay for smooth observable, etc.).
##### Scheda breve Scheda completa Scheda completa (DC)
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - Fisica Matematica
English
Con Impact Factor ISI
http://www.mat.uniroma2.it/~liverani/Lavori/live0401.pdf
Liverani, C., Gouezel, S. (2006). Banach spaces adapted to Anosov systems. ERGODIC THEORY & DYNAMICAL SYSTEMS, 26(1), 189-217 [10.1017/S0143385705000374].
Liverani, C; Gouezel, S
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/37016
• ND
• 160
• 153