We 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 mo- menta, then the asymptotic Maslov indices of periodic orbits are dense in the half line [0, +∞). Furthermore, if the Hamiltonian is the Fenchel dual of an electromagnetic Lagrangian, then 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 asymp- totic Maslov index by the analogue of Mather’s theory of the beta function, the asymptotic Maslov index playing the role of the rotation vector.
|Autori:||ABBONDANDOLO A; A. FIGALLI|
|Titolo:||Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index|
|Anno del prodotto:||2008|
|Digital Object Identifier (DOI):||10.1007/s11784-008-0057-6|
|Appare nelle tipologie:||1.1 Articolo in rivista|