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Rigidity in topology C^0 of the Poisson bracket for Tonelli Hamiltonians
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 …