Israel Journal of Mathematics

, Volume 59, Issue 1, pp 64–80 | Cite as

Generic properties of invariant measures for simple piecewise monotonic transformations

  • Franz Hofbauer


We endow the set of all invariant measures of topologically transitive subsetsL of certain piecewise monotonic transformations on [0, 1] with the weak topology. We show that the set of periodic orbit measures is dense, that the sets of ergodic, of nonatomic, and of measures with supportL are dense-sets, that the se of strongly mixing measures is of first category, and that the set of measures with zero entropy contains a denseGin/gd-set.


Periodic Orbit Invariant Measure Periodic Point Closed Path Oriented Graph 
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Copyright information

© Hebrew University 1987

Authors and Affiliations

  • Franz Hofbauer
    • 1
  1. 1.Institut für MathematikUniversität WienWienAustria

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