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We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study $\mathcal… Click to show full abstract
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study $\mathcal F$-hypercyclicity for two families of subsets of the natural numbers associated to the existence of arbitrary long arithmetic progressions. We investigate their connection with different concepts in linear dynamics. We also prove that one of these notions characterize multiple recurrent hypercyclic operators.
Keywords:
chaos linear;
progressions chaos;
linear dynamics;
arithmetic progressions
Journal Title: Integral Equations and Operator Theory
Year Published: 2022
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Journal Title: Integral Equations and Operator Theory
Year Published: 2022
Link to full text (if available)
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recommendations!