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math.DS2010★ 24 cited
Lecture notes on Mather's theory for Lagrangian systems
Alfonso Sorrentino
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Università deg…
math.DS2010★ 7 cited
Weak Liouville-Arnold Theorems & Their Implications
Leo T. Butler, Alfonso Sorrentino
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n indep…
math.SG2010★ 9 cited
Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms
Alfonso Sorrentino, Claude Viterbo
In this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at 0 of Mather's $β…