Young towers for product systems

Stefano  Luzzatto; Marks  Ruziboev

doi:10.3934/dcds.2016.36.1465

Article Contents

2016, Volume 36, Issue 3: 1465-1491. Doi: 10.3934/dcds.2016.36.1465

This issue Previous Article Positive solutions of a nonlinear Schrödinger system with nonconstant potentials Next Article One smoothing property of the scattering map of the KdV on $\mathbb{R}$

Young towers for product systems

Stefano Luzzatto^1, and
Marks Ruziboev^2,

1.
International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste
2.
International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste

Received: February 2015

Revised: June 2015

Published: May 2017

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Abstract

We show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, Hénon maps and partially hyperbolic systems.

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Mathematics Subject Classification: Primary: 37A05, 37A25.

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