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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
c 0 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
© 2024 MSP (Mathematical Sciences
Publishers).