Density of fiberwise orbits in minimal iterated function systems on the circle

Pablo G. Barrientos; Abbas Fakhari; Aliasghar Sarizadeh

doi:10.3934/dcds.2014.34.3341

Article Contents

2014, Volume 34, Issue 9: 3341-3352. Doi: 10.3934/dcds.2014.34.3341

This issue Previous Article A Liouville-type theorem for higher order elliptic systems Next Article Homoclinic orbits of first-order superquadratic Hamiltonian systems

Density of fiberwise orbits in minimal iterated function systems on the circle

1.
Instituto de Matemática e Estatística, UFF, Rua Mário Santos Braga s/n - Campus Valonguinhos, Niterói
2.
Department of Mathematics, Shahid Beheshti University, G.C.Tehran 19839
3.
Department of Mathematics, Ilam University, P.O. Box 69315-516, Ilam

Received: July 31, 2013

Revised: December 31, 2013

Published: August 2014

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Abstract

We study the minimality of almost every orbital branch of minimal iterated function systems (IFSs). We prove that this kind of minimality holds for forward and backward minimal IFSs generated by orientation-preserving homeomorphisms of the circle. We provide new examples of iterated functions systems where this behavior persists under perturbation of the generators.

Keywords:

Minimal IFS on the circle,
minimality of orbital branches (fiberwise orbits).

Mathematics Subject Classification: Primary: 37C05, 37C20; Secondary: 37E10.

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