Journal of Modern Dynamics (JMD)

There exists an interval exchange with a non-ergodic generic measure

Pages: 289 - 304, Volume 9, 2015      doi:10.3934/jmd.2015.9.289

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Jon Chaika - Department of Mathematics, University of Utah, 155 S. 1400 E., Room 233, Salt Lake City, UT 84112, United States (email)
Howard Masur - Department of Mathematics, University of Chicago, 5734 S. University Avenue, Room 208C, Chicago, IL 60637, United States (email)

Abstract: We prove that there exists an interval exchange transformation and a point so that the orbit of the point equidistributes according to a non-ergodic measure. That is, it is possible for a non-ergodic measure to arise from the Krylov-Bogolyubov construction of invariant measures for an interval exchange transformation.

Keywords:  Interval exchanges, generic points, Rauzy induction.
Mathematics Subject Classification:  Primary: 37E05.

Received: November 2014;      Revised: July 2015;      Available Online: October 2015.