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Persistence of wandering intervals in self-similar affine interval exchange transformations

Published online by Cambridge University Press:  23 June 2009

XAVIER BRESSAUD ,
PASCAL HUBERT  and
ALEJANDRO MAASS
XAVIER BRESSAUD
Affiliation:
Université Paul Sabatier, Institut de Mathématiques de Toulouse, F-31062 Toulouse Cedex, France (email: [email protected])
PASCAL HUBERT
Affiliation:
Laboratoire Analyse, Topologie et Probabilités, Case cour A, Faculté des Sciences de Saint-Jerôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France (email: [email protected])
ALEJANDRO MAASS
Affiliation:
Centro de Modelamiento Matemático and Departamento de Ingeniería Matemática, Universidad de Chile, Av. Blanco Encalada 2120, Santiago, Chile (email: [email protected])
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Abstract

In this article we prove that given a self-similar interval exchange transformation T(λ,π), whose associated matrix verifies a quite general algebraic condition, there exists an affine interval exchange transformation with wandering intervals that is semi-conjugated to it. That is, in this context the existence of Denjoy counterexamples occurs very often, generalizing the result of Cobo [Piece-wise affine maps conjugate to interval exchanges. Ergod. Th. & Dynam. Sys.22 (2002), 375–407].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 3 , June 2010 , pp. 665 - 686
Copyright
Copyright © Cambridge University Press 2009

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