Unique ergodicity of circle and interval exchange transformations with flips
C. Gutierrez, S. Lloyd, V. Medvedev, B. Pires, E. Zhuzhoma
TL;DR
This paper investigates the conditions under which transitive exchange maps with flips exist on the unit circle, providing a complete characterization based on the number of subintervals and flips.
Contribution
It offers a comprehensive classification of transitive exchange maps with flips on the circle, answering a key open question in the field.
Findings
Characterization of when transitive exchange maps with flips exist
Complete answer to existence question based on parameters n and f
Advances understanding of ergodic properties of interval exchange transformations
Abstract
We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange map of the unit circle defined on n subintervals and having f flips.
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Taxonomy
TopicsMathematical Dynamics and Fractals · semigroups and automata theory · Advanced Topology and Set Theory