Abstract : We prove the following rigidity result for the Tonelli Hamiltonians. Let T * M be the cotangent bundle of a closed manifold M endowed with its usual symplectic form. Let (F_n) be a sequence of Tonelli Hamiltonians that C^0 converges on the compact subsets to a Tonelli Hamiltonian F. Let (G_n) be a sequence of Hamiltonians that that C^0 converges on the compact subsets to a Hamiltonian G. We assume that the sequence of the Poisson brackets ({F_n , G_n }) C^0-converges on the compact subsets to a C^1 function H. Then H = {F, G}.
https://hal-univ-avignon.archives-ouvertes.fr/hal-01154913
Contributor : Marie-Claude Arnaud <>
Submitted on : Monday, May 25, 2015 - 4:47:20 PM Last modification on : Tuesday, December 8, 2020 - 10:12:03 AM Long-term archiving on: : Tuesday, September 15, 2015 - 6:49:36 AM