Set-Valued Chaos in Linear Dynamics
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DOI: 10.1007/s00020-017-2394-6
Abstract: We study several notions of chaos for hyperspace dynamics associated to continuous linear operators. More precisely, we consider a continuous linear operator $$T : X \rightarrow X$$T:X→X on a topological vector space X, and the… read more here.
Keywords: space; chaos linear; set valued; valued chaos ... See more keywords
Arithmetic Progressions and Chaos in Linear Dynamics
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DOI: 10.1007/s00020-022-02687-3
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… read more here.
Keywords: chaos linear; progressions chaos; linear dynamics; arithmetic progressions ... See more keywords