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January  2010, 26(1): 251-263. doi: 10.3934/dcds.2010.26.251

Transitive circle exchange transformations with flips

Carlos Gutierrez 1, , Simon Lloyd 2, , Vladislav Medvedev 3, , Benito Pires 4, and  Evgeny Zhuzhoma 5,

1. 

ICMC-USP, São Carlos, Caixa Postal 668, CEP 13560-970, São Carlos, SP
2. 

School of Mathematics and Statistics, University of New South Wales, Sydney
3. 

Institute of Applied Mathematics and Cybernetics, Nizhny Novgorod State University, Nizhny Novgorod, Russian Federation
4. 

Departamento de Física e Matemática, Universidade de São Paulo, Ribeirão Preto - SP, Brazil
5. 

Department of Mathematics and Physics, Nizhny Novgorod State Pedagogical University, Nizhny Novgorod, Russian Federation

Received  October 2008 Revised  June 2009 Published  October 2009

We study the existence of transitive exchange transformations with flips defined on the unit circle $S^1$. We provide a complete answer to the question of whether there exists a transitive exchange transformation of $S^1$ defined on $n$ subintervals and having $f$ flips.
Keywords: orientation reversing., interval exchange transformation, Rauzy induction.
Mathematics Subject Classification: Primary: 37E05; 37E10 Secondary: 37.
Citation: Carlos Gutierrez, Simon Lloyd, Vladislav Medvedev, Benito Pires, Evgeny Zhuzhoma. Transitive circle exchange transformations with flips. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 251-263. doi: 10.3934/dcds.2010.26.251
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