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

Ian Curtis, Sean Griswold, Abigail Halverson, Eric Stilwell, Sarah Teske, David Walmsley and Shaozhe Wang

Vol. 17 (2024), No. 3, 531–541
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 p or c0 there is a weighted backward shift which is strongly topologically transitive but not mixing.

Keywords
hypercyclicity, dynamical systems, hypermixing, strong topological transitivity
Mathematical Subject Classification
Primary: 37B02, 47A16
Milestones
Received: 13 January 2023
Revised: 13 March 2023
Accepted: 16 March 2023
Published: 17 July 2024

Communicated by Stephan Garcia
Authors
Ian Curtis
St. Olaf College
Northfield, MN
United States
Sean Griswold
St. Olaf College
Northfield, MN
United States
Abigail Halverson
St. Olaf College
Northfield, MN
United States
Eric Stilwell
St. Olaf College
Northfield, MN
United States
Sarah Teske
St. Olaf College
Northfield, MN
United States
David Walmsley
Department of Mathematics, Statistics and Computer Science
St. Olaf College
Northfield, MN
United States
Shaozhe Wang
St. Olaf College
Northfield, MN
United States