A graph-theoretic bound on the number of independent absolutely continuous invariant measures
For piecewise expanding interval maps with slope \(>2\) the authors derive upper bounds on the number of absolutely continuous ergodic invariant measures. These bounds are based on the accessibility graph of the intervals of monotonicity of the transformation. Random compositions of such maps are treated by the same approach. For individual maps a sharper, but not so easily computable bound, based on the Markov diagram of such maps, can be found in section 4 of \textit{F. Hofbauer} [Ergodic Theory Dyn. Syst. 1, 159-178 (1981; Zbl 0474.28007)].
absolutely continuous ergodic invariant measures
scientific article; zbMATH DE number 4105280
scientific article