Pomeau-Manneville maps are global-local mixing

Claudio Bonanno; Marco Lenci

doi:10.3934/dcds.2020309

Article Contents

2021, Volume 41, Issue 3: 1051-1069. Doi: 10.3934/dcds.2020309

This issue Previous Article Properties of the minimizers for a constrained minimization problem arising in Kirchhoff equation Next Article Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials

Pomeau-Manneville maps are global-local mixing

Claudio Bonanno^1, , and
Marco Lenci^2,

1.
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
2.
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy, and, Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy

^* Corresponding author: Claudio Bonanno
^* Corresponding author: Claudio Bonanno

Received: March 2020

Revised: June 2020

Early access: August 2020

Published: March 2021

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Abstract

We prove that a large class of expanding maps of the unit interval with a $ C^2 $-regular indifferent fixed 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.

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Mathematics Subject Classification: Primary:37A40, 37A25, 37E05;Secondary:37D25, 37C25.

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References

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