We study a class of two-dimensional partially hyperbolic systems, not necessarily skew products, in an attempt to develop a general theory. As a main result, we provide explicit conditions for the existence of finitely many physical measures (and SRB) and prove exponential decay of correlations for mixing measures. In addition, we obtain precise information on the regularity of such measures (they are absolutely continuous with respect to Lebesgue with density in some Sobolev space). To illustrate the scope of the theory, we show that our results apply to the case of fast-slow partially hyperbolic systems, and for such systems we obtain more precise results on the structure of the SRB measures.

Castorrini, R., Liverani, C. (2022). Quantitative statistical properties of two-dimensional partially hyperbolic systems. ADVANCES IN MATHEMATICS, 409 [10.1016/j.aim.2022.108625].

Quantitative statistical properties of two-dimensional partially hyperbolic systems

Liverani C.
Membro del Collaboration Group
2022-01-01

Abstract

We study a class of two-dimensional partially hyperbolic systems, not necessarily skew products, in an attempt to develop a general theory. As a main result, we provide explicit conditions for the existence of finitely many physical measures (and SRB) and prove exponential decay of correlations for mixing measures. In addition, we obtain precise information on the regularity of such measures (they are absolutely continuous with respect to Lebesgue with density in some Sobolev space). To illustrate the scope of the theory, we show that our results apply to the case of fast-slow partially hyperbolic systems, and for such systems we obtain more precise results on the structure of the SRB measures.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
Partially hyperbolic map; Slow-fast system; Decay of correlation; Transfer operator
Castorrini, R., Liverani, C. (2022). Quantitative statistical properties of two-dimensional partially hyperbolic systems. ADVANCES IN MATHEMATICS, 409 [10.1016/j.aim.2022.108625].
Castorrini, R; Liverani, C
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
advances.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 1.62 MB
Formato Adobe PDF
1.62 MB 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/2108/312283
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact