We study the properties of 'infinite-volume mixing' for two classes of intermittent maps: expanding maps [0,1]--> [0,1] with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps R^+-->R^+ with an indifferent fixed point at infinity preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. The first subclass includes, among others, the Farey map. The second class includes the standard Pomeau–Manneville map x-->x+x^2 mod 1. Morevoer, we use global-local mixing to prove certain limit theorems for our intermittent maps.

Infinite mixing for one-dimensional maps with an indifferent fixed point

C. Bonanno;P. Giulietti;
2018

Abstract

We study the properties of 'infinite-volume mixing' for two classes of intermittent maps: expanding maps [0,1]--> [0,1] with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps R^+-->R^+ with an indifferent fixed point at infinity preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. The first subclass includes, among others, the Farey map. The second class includes the standard Pomeau–Manneville map x-->x+x^2 mod 1. Morevoer, we use global-local mixing to prove certain limit theorems for our intermittent maps.
Bonanno, C.; Giulietti, P.; Lenci, M.
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: http://hdl.handle.net/11568/932782
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 3
social impact