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A dynamical condition for differentiability of Mather's average action

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  • We prove the differentiability of Mather's average action on all rotation vectors of measures whose supports are contained in a Lipschitz Lagrangian asymptotically isolated graph, invariant by Tonelli Hamiltonians. We also show the relationship between differentiability of $\beta $ and local integrability of the Hamiltonian flow.
    Mathematics Subject Classification: Primary: 37J50, 37J15; Secondary: 37J35.


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