Pomeau-Manneville maps are global-local mixing

preprint2020arXivOpen access

Abstract

We prove that a large class of expanding maps of the unit interval with a C2C^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+xp+1T(x) = x + x^{p+1} mod 1 (p≥1p \ge 1), the Liverani-Saussol-Vaienti maps (with index p≥1p \ge 1) and many generalizations thereof.

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