Israel Journal of Mathematics

, Volume 34, Issue 3, pp 213–237

On intrinsic ergodicity of piecewise monotonic transformations with positive entropy

  • Franz Hofbauer
Article

DOI: 10.1007/BF02760884

Cite this article as:
Hofbauer, F. Israel J. Math. (1979) 34: 213. doi:10.1007/BF02760884

Abstract

We consider a class of piecewise monotonically increasing functionsf on the unit intervalI. We want to determine the measures with maximal entropy for these transformations. In part I we construct a shift-space Σf+ isomorphic to (I, f) generalizing the \-shift and another shift ΣM over an infinite alphabet, which is of finite type given by an infinite transition matrixM. ΣM has the same set of maximal measures as (I, f) and we are able to compute the maximal measures of maximal measures of. In part II we try to bring these results back to (I, f). There are only finitely many ergodic maximal measures for (I, f). The supports of two of them have at most finitely many points in common. If (I, f) is topologically transitive it has unique maximal measure.

Copyright information

© Hebrew University 1979

Authors and Affiliations

  • Franz Hofbauer
    • 1
  1. 1.Mathematisches Instittut der Universität WienWienAustria