Pomeau-Manneville maps are global-local mixing

TL;DR

This paper proves that a broad class of Pomeau-Manneville maps, including standard and generalized versions, exhibit global-local mixing behavior, advancing understanding of their statistical properties.

Contribution

The paper establishes the global-local mixing property for a wide class of expanding maps with indifferent points, including standard and generalized Pomeau-Manneville maps.

Findings

Proves global-local mixing for Pomeau-Manneville maps

Includes maps with indifferent fixed points and full increasing branches

Extends previous results to a broader class of maps

Abstract

We prove that a large class of expanding maps of the unit interval with a $C^2$-regular indifferent point in 0 and full increasing branches are global-local mixing. This class includes the standard Pomeau-Manneville maps $T(x) = x + x^{p+1}$ mod 1 ($p \ge 1$), the Liverani-Saussol-Vaienti maps (with index $p \ge 1$) and many generalizations thereof.