Smoothness of densities of semigroups of measures on homogeneous groups

Jacek Dziubański; Jacek Zienkiewicz

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Density of periodic orbit measures for transformations on the interval with two monotonic pieces

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Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and $h_{t o p} (T) > 0$ , it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.