Expanding actions: minimality and ergodicity-Reference-Cited by-同舟云学术

Expanding actions: minimality and ergodicity

Published:2017-05-04 Issue:04 Volume:17 Page:1750031
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

Barrientos Pablo G.¹,Fakhari Abbas²,Malicet Dominique³,Sarizadeh Aliasghar⁴

Affiliation:

1. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Rua Mário Santos Braga s/n - Campus Valonguinhos, Niterói, Brazil

2. Department of Mathematics, Shahid Beheshti University, Tehran 19839, Iran

3. Instituto de Matemática e Estatística, Universidade Estadual de Rio de Janeiro, Rua São Francisco Xavier, 524, Maracanã, Rio de Janeiro, Brazil

4. Department of Mathematics, Ilam University, Ilam, Iran

Abstract

We prove that every expanding minimal semigroup action of [Formula: see text] diffeomorphisms of a compact manifold (resp. [Formula: see text] conformal) is robustly minimal (resp. ergodic with respect to the Lebesgue emeasure). We also show how, locally, a blending region yields the robustness of the minimality and implies ergodicity.

Funder

Secretaría de Estado de Investigación, Desarrollo e Innovación (ES)

Institute for Research in Fundamental Sciences

Conselho Nacional de Desenvolvimento Científico e Tecnológico

CAPES

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493717500319

Reference21 articles.

1. Symbolic blender-horseshoes and applications

2. Dynamics of iterated function systems on the circle close to rotations

3. Robust vanishing of all Lyapunov exponents for iterated function systems

4. Iterated Random Functions

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