# 北海道力学系webセミナー: Absolutely continuous $\sigma$-finite invariant measures for weakly expanding random maps with a flat point (豊川 永喜（九州大学 マス・フォア・インダストリ研究所）)

2021年64日 開催

Time：2021年6月4日(金)　13:00～14:00

Speaker：豊川 永喜（九州大学 マス・フォア・インダストリ研究所）

Title： Absolutely continuous $\sigma$-finite invariant measures for weakly expanding random maps with a flat point

Abstract：In this talk, we show necessary and sufficient conditions for the existence of an absolutely continuous $\sigma$-finite invariant measure with a certain support property for a given Markov operator. One of the equivalent conditions is weak almost periodicity of a jump operator of the original Markov operator which arises the well-known Jacobs–de Leeuw–Glicksberg splitting. As an application, we estimate invariant density functions for several random maps on the unit interval which have both a common indifferent fixed point and uniformly contracting branches (or moreover a flat point).

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