Discontinuity growth of interval exchange maps

2008/11/06 by Christopher F. Novak, Novak, Christopher F.
Mathematics · #20F28 (Secondary) #37E05 (Primary) 37C85 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #math.DS #math.GR #msc:20F28 #msc:37C85 #msc:37E05

paper · pdf · doi:10.48550/arxiv.0811.1014

32 pages, 5 figures

arxiv created 2008/11/06 · arxiv updated 2009/12/01

Abstract

For an interval exchange map, the number of discontinuities of its iterates either exhibits linear growth or is bounded. This dichotomy is used to prove that the group of interval exchanges does not contain distortion elements, giving examples of groups that do not act faithfully via interval exchanges. As a further application of this dichotomy, a classification of centralizers in the group of interval exchanges is given. This classification of centralizers is used to compute the automorphism group of the interval exchange group.

Related

• Discrepancy Properties and Conjugacy Classes of Interval Exchange Transformations
• Relations with a fixed interval exchange transformation
• Notes on the commutator group of the group of interval exchange transformations
• Distortion in the group of locally monotone homeomorphisms of a Cantor set and in the group of generalized interval exchange transformations
• Asymptotic Pairs for Interval Exchange Transformations