Generic properties of invariant measures for simple piecewise monotonic transformations
- 78 Downloads
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.
KeywordsPeriodic Orbit Invariant Measure Periodic Point Closed Path Oriented Graph
Unable to display preview. Download preview PDF.
- 6.F. Hofbauer,Kneading invariants and Markov diagrams, inErgodic Theory and Related Topics. Proceedings (H. Michel, ed.), Akademie-Verlag, Berlin, 1982.Google Scholar