On Periods of Interval Exchange Transformations

Jose S. Cánovas, Antonio Linero Bas and Gabriel Soler López
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Jose S. Cánovas: Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30202 Cartagena, Spain
Antonio Linero Bas: Department of Mathematics, University of Murcia, 30100 Murcia, Spain
Gabriel Soler López: Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30202 Cartagena, Spain

Mathematics, 2022, vol. 10, issue 9, 1-32

Abstract: In this paper, we study the periods of interval exchange transformations. First, we characterize the periods of interval exchange transformations with one discontinuity. In particular, we prove that there is no forcing between periods of maps with two branches of continuity. This characterization is a partial solution to a problem by Misiurewicz. In particular, a periodic structure is not possible for a family of the maps with one point of discontinuity in which the monotonicity changes. Second, we study a similar problem for interval exchange transformations with two discontinuities. Here we classify these maps in several classes such that two maps in the same class have the same periods. Finally, we study the set of periods for two categories, obtaining partial results that prove that the characterization of the periods in each class is not an easy problem.

Keywords: periodic orbits; noncontinuous interval maps; forcing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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