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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 |
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Vol. 17 (2024), No. 3, 531–541
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Abstract |
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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 or there is a weighted backward shift which is strongly topologically transitive but not mixing. |
Keywords
hypercyclicity, dynamical systems, hypermixing, strong
topological transitivity
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Mathematical Subject Classification
Primary: 37B02, 47A16
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Milestones
Received: 13 January 2023
Revised: 13 March 2023
Accepted: 16 March 2023
Published: 17 July 2024
Communicated by Stephan Garcia
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Authors |
| Ian Curtis | |
| St. Olaf College Northfield, MN United States |
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| Sean Griswold | |
| St. Olaf College Northfield, MN United States |
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| Abigail Halverson | |
| St. Olaf College Northfield, MN United States |
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| Eric Stilwell | |
| St. Olaf College Northfield, MN United States |
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| Sarah Teske | |
| St. Olaf College Northfield, MN United States |
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| David Walmsley | |
| Department of Mathematics,
Statistics and Computer Science St. Olaf College Northfield, MN United States |
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| Shaozhe Wang | |
| St. Olaf College Northfield, MN United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
