Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index

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dc.creatorAbbondandolo, Alberto
dc.creatorFigalli, Alessio
dc.date2007-09-29
dc.date2008-01-19
dc.date.accessioned2026-07-07T12:20:59Z
dc.date.available2026-07-07T12:20:59Z
dc.descriptionWe study the properties of the asymptotic Maslov index of invariant measures for time-periodic Hamiltonian systems on the cotangent bundle of a compact manifold M. We show that if M has finite fundamental group and the Hamiltonian satisfies some general growth assumptions on the momenta, the asymptotic Maslov indices of periodic orbits are dense in the positive half line. Furthermore, if the Hamiltonian is the Fenchel dual of an electro-magnetic Lagrangian, every non-negative number r is the limit of the asymptotic Maslov indices of a sequence of periodic orbits which converges narrowly to an invariant measure with asymptotic Maslov index r. We discuss the existence of minimal ergodic invariant measures with prescribed asymptotic Maslov index by the analogue of Mather's theory of the beta function, the asymptotic Maslov index playing the role of the rotation vector.
dc.description21 pages, final version
dc.identifierhttps://arxiv.org/abs/0710.0067
dc.identifierhttp://arxiv.org/abs/0710.0067
dc.identifierJournal of Fixed Point Theory and Applications 3 (2008), 95-120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213228
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject37J05; 37J45; 37J50
dc.titleInvariant measures of Hamiltonian systems with prescribed asymptotic Maslov index
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