Mathematics – Dynamical Systems
Scientific paper
2007-09-29
Journal of Fixed Point Theory and Applications 3 (2008), 95-120
Mathematics
Dynamical Systems
21 pages, final version
Scientific paper
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 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.
Abbondandolo Alberto
Figalli Alessio
No associations
LandOfFree
Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-462190