We consider maps preserving a foliation which is uniformly contracting and a one-dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for suitable Poincaré maps of a large class of singular hyperbolic flows. From this we deduce a logarithm law for these flows.

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

GALATOLO, STEFANO;
2014-01-01

Abstract

We consider maps preserving a foliation which is uniformly contracting and a one-dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for suitable Poincaré maps of a large class of singular hyperbolic flows. From this we deduce a logarithm law for these flows.
2014
Vitor, Araújo; Galatolo, Stefano; Maria José, Pacifico
File in questo prodotto:
File Dimensione Formato  
CorrDecayUnifContrFibersLogLawSingHyp_Personal-Araujo-Galatolo-Pacifico.pdf

solo utenti autorizzati

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 621.86 kB
Formato Adobe PDF
621.86 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/11568/388267
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
social impact