Strong topological transitivity, hypermixing, and their relationships with other dynamical properties

2023/04/04 by Ian S. Curtis, Sean Griswold, Curtis, Ian +11
Computer Science · Mathematics · #47A16 (Primary) 37B02 (Secondary) #Advanced Topology and Set Theory #Cellular Automata and Applications #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2304.02073

openalex publication_date 2023/04/04 · openalex created_date 2023/04/07 · openalex updated_date 2026/07/28

Abstract

Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger version of the mixing property. We continue the investigation of these notions with two main results. First, we show there are dynamical systems which are strongly topologically transitive but not weakly mixing. We then show that on ℓ^p or c₀, there is a weighted backward shift which is strongly topologically transitive but not mixing.

Related

• Conceptions of Topological Transitivity
• Transitivity and Mixing Properties of Set-Valued Dynamical Systems
• Types of mixings and transitivities in topological dynamics
• Varieties of Mixing
• Variations on the Concept of Topological Transitivity