1 0 Ju l 2 00 8 The Dynamics of Pseudographs in Convex Hamiltonian Systems 1
نویسنده
چکیده
mechanisms 26 5 The relation and its dynamical consequences . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6 Evolution operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 7 Coverings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 8 Mather’s mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 9 Arnold’s mechanism for systems with finitely many static classes . . . . . . . . . . . . . . . 36 Applications 41 10 Twist Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 11 Generalized Arnold Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Appendix 43 A Semi-concave functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 B Uniform families of Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 MSC: 37J40, 37J50
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متن کاملThe dynamics of pseudographs in convex Hamiltonian systems
We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They emerge in a natural way from Fathi’s weak KAM theory. By this method, we find various orbits which connect prescribed regions of the phase space. Our study is...
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