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DTSTART:20160101T000000
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DTSTART;TZID=UTC:20170912T163000
DTEND;TZID=UTC:20170912T173000
DTSTAMP:20211006T215857Z
CREATED:20211006T215857Z
LAST-MODIFIED:20211006T215857Z
UID:20168-1505233800-1505237400@www.ashoka.edu.in
SUMMARY:Dario Darji\, University of Liouville\, USA
DESCRIPTION:Abstract: In the early 1970’s Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity\, supercyclicity\, Li-Yorke chaos and shadowing. In the case that the Banach space is $c_0$ or $undefinedell_p$ ($1 undefinedleq p < undefinedinfty$)\, we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover\, we study various notions of shadowing for operators on Banach spaces. In particular\, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This contrasts with the expected results for nonlinear dynamics on compact manifolds\, illuminating the richness of dynamics of infinite dimensional linear operators.\n 
URL:https://www.ashoka.edu.in/event/dario-darji-university-of-liouville-usa/
CATEGORIES:Offline
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