Asymptotic periodicity of the iterates of weakly constrictive Markov operators
A Markov operator \(P: L^ 1\to L^ 1\) is said weakly constrictive if there exists a weakly compact set \(f\subset L^ 1\) which is an attractor for trajectories \(p^ nf\) of all densities \(f\in L^ 1\). This property is proved to be a sufficient condition for asymptotic periodicity of all \(p^ nf\), \(f\in L^ 1\). It is a generalization of the main result of [\textit{A. Lasota}, \textit{T. Y. Li} and \textit{J. A. Yorke}, Trans. Am. Math. Soc. 286, 751-764 (1984; Zbl 0564.47015)], where strong constrictivity is assumed.
scientific article; zbMATH DE number 3925629