Dynamics of induced homeomorphisms of one-dimensional solenoids

Francisco J. López-Hernández

doi:10.3934/dcds.2018185

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2018, Volume 38, Issue 9: 4243-4257. Doi: 10.3934/dcds.2018185

This issue Previous Article Next Article On the arithmetic difference of middle Cantor sets

Dynamics of induced homeomorphisms of one-dimensional solenoids

Francisco J. López-Hernández

Centro de Investigación en Matemáticas, A.C., Jalisco S/N, Col. Valenciana CP: 36023, Guanajuato, Gto, México

Received: March 31, 2017

Revised: September 30, 2017

Published: August 2018

This paper is part of the author's doctoral dissertation. Research was supported by CONACyT scholarship for Doctoral Students

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Abstract

We study the displacement function of homeomorphisms isotopic to the identity of the universal one-dimensional solenoid and we get a characterization of the lifting property for an open and dense subgroup of the isotopy component of the identity. The dynamics of an element in this subgroup is also described using rotation theory.

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Mathematics Subject Classification: Primary: 22Cxx, 37Bxx.

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