A dynamical condition for differentiability of Mather's average action

Abstract

We prove the differentiability of $\beta$ of Mather function on all homology classes corresponding to rotation vectors of measures whose supports are contained in a Lipschitz Lagrangian absorbing graph, invariant by Tonelli Hamiltonians. We also show the relationship between local differentiability of $\beta$ and local integrability of the Hamiltonian flow.

22 pages, 1 figure

Cited by in corpus (1)

• Tonelli Lagrangian systems on the 2-torus and topological entropy