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arXiv · 1708.09369

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

Claudio Bonanno·Paolo Giulietti·Marco Lenci
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Abstract

We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps $\mathbb{R}^+ \longrightarrow \mathbb{R}^+$ with an indifferent fixed point at $+\infty$ 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 $x \mapsto x+x^2$ mod 1. Morevoer, we use global-local mixing to prove certain limit theorems for our intermittent maps.

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Claudio Bonanno, Paolo Giulietti, Marco Lenci. 2017-08-30. Infinite mixing for one-dimensional maps with an indifferent fixed point. https://doi.org/10.1088/1361-6544/aadc04

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