DCDS
Transitive circle exchange transformations with flips
Carlos Gutierrez Simon Lloyd Vladislav Medvedev Benito Pires Evgeny Zhuzhoma
Discrete & Continuous Dynamical Systems - A 2010, 26(1): 251-263 doi: 10.3934/dcds.2010.26.251
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

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