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 + ∞ 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 / Bonanno, Claudio; Giulietti, Paolo; Lenci, Marco. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 31:11(2018), pp. 5180-5213. [10.1088/1361-6544/aadc04]

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

Lenci, Marco
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 + ∞ 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.
2018
Infinite mixing for one-dimensional maps with an indifferent fixed point / Bonanno, Claudio; Giulietti, Paolo; Lenci, Marco. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 31:11(2018), pp. 5180-5213. [10.1088/1361-6544/aadc04]
Bonanno, Claudio; Giulietti, Paolo; Lenci, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/649079
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