C^0-rigidity of Poisson brackets

dc.creatorEntov, Michael
dc.creatorPolterovich, Leonid
dc.date2007-12-18
dc.date.accessioned2026-07-07T08:49:52Z
dc.date.available2026-07-07T08:49:52Z
dc.descriptionConsider a functional associating to a pair of compactly supported smooth functions on a symplectic manifold the maximum of their Poisson bracket. We show that this functional is lower semi-continuous with respect to the product uniform (C^0) norm on the space of pairs of such functions. This extends previous results of Cardin-Viterbo and Zapolsky. The proof involves theory of geodesics of the Hofer metric on the group of Hamiltonian diffeomorphisms. We also discuss a failure of a similar semi-continuity phenomenon for multiple Poisson brackets of three or more functions.
dc.descriptionLatex, 11 pages
dc.identifierhttps://arxiv.org/abs/0712.2913
dc.identifierhttp://arxiv.org/abs/0712.2913
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144458
dc.subjectSymplectic Geometry
dc.subjectClassical Analysis and ODEs
dc.subject53D35, 53D05
dc.titleC^0-rigidity of Poisson brackets
dc.typetext

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