37 citations · 126 across the 20 of their papers we have counts for
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On the fragility of periodic tori for families of symplectic twist maps
Marie-Claude Arnaud, Jessica Elisa Massetti, Alfonso Sorrentino
In this article we study the fragility of Lagrangian periodic tori for symplectic twist maps of the -dimensional annulus and prove a rigidity result for completely integrable o…
Aubry-Mather theory on graphs
Antonio Siconolfi, Alfonso Sorrentino
We formulate Aubry-Mather theory for Hamiltonians/Lagrangians defined on graphs and discuss its relationship with weak KAM theory developed in [24].
On the rigidity of integrable deformations of twist maps and Hamiltonian flows
Jessica Elisa Massetti, Alfonso Sorrentino
In this article we investigate rigidity properties of integrable area-preserving twist maps of the cylinder. More specifically, we prove that if a deformation of the standard integ…
Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle
Stefano Galatolo, Alfonso Sorrentino
We prove quantitative statistical stability results for a large class of small perturbations of circle diffeomorphisms with irrational rotation numbers. We show that if the…
On the regularity of Mather's -function for standard-like twist maps
Carlo Carminati, Stefano Marmi, David Sauzin +1
We consider the minimal average action (Mather's function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations…
Markov Numbers, Mather's function and stable norm
Alfonso Sorrentino, Alexander P. Veselov
V. Fock [7] introduced an interesting function , related to Markov numbers. We explain its relation to Federer-Gromov's stable norm and Mather's -funct…