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math.DS2009
Differentiability of Mather's average action and integrability on closed surfaces
Daniel Massart, Alfonso Sorrentino
In this article we study the differentiability of Mather's -function on closed surfaces and its relation to the integrability of the system.
math.DS2009
On the Integrability of Tonelli Hamiltonians
Alfonso Sorrentino
In this article we discuss a weaker version of Liouville's theorem on the integrability of Hamiltonian systems. We show that in the case of Tonelli Hamiltonians the involution hypo…