2006/07/18 by Eduard Kontorovich, Michael Megrelishvili, Kontorovich, Eduard +1
Mathematics · #37Bxx #54H15 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #General Topology (math.GN) #Mathematical Dynamics and Fractals #math.DS #math.GN #msc:37Bxx #msc:54H15
paper · pdf · doi:10.48550/arxiv.math/0607440
7 pages
arxiv created 2006/07/18 · openalex publication_date 2006/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that for a transitive dynamical system (X,f) sensitivity to initial conditions follows from the assumption that the periodic points are dense. This was done by several authors: Banks, Brooks, Cairns, Davis and Stacey, Silverman, and also by Glasner and Weiss. In the latter article Glasner and Weiss established a stronger result (for compact metric systems) which implies that a transitive non-minimal compact metric system (X,f) with dense set of almost periodic points is sensitive. This is true also for group actions as was proved in a recent book of Glasner. Our aim is to generalize these results in the frame of a unified approach for a wide class of topological semigroup actions including one-parameter semigroup actions on Polish spaces.