[1]     Alfonso Sorrentino.

          On the total disconnectedness of the quotient Aubry set.

          Ergodic Theory Dynam. Systems 28 (1): 267 - 290, 2008.

[2]     Alfonso Sorrentino.

          On the structure of action-minimizing sets for Lagrangian systems.

          Ph.D. thesis, Princeton University, 157 pp. ISBN: 978-0549-52575-2, ProQuest LLC, 2008.

[3]     Albert Fathi, Alessandro Giuliani and Alfonso Sorrentino.

          Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class.

           Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. VIII (4): 659 - 680, 2009.

[4]     Alfonso Sorrentino and Claude Viterbo.

          Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms.

          Geom. & Topol. 14 (4): 2383 - 2403, 2010.

[5]     Alfonso Sorrentino.

          On the integrability of Tonelli Hamiltonians.

          Trans. Amer. Math. Soc. 363 (10): 5071 - 5089, 2011.

[6]     Daniel Massart and Alfonso Sorrentino.

          Differentiability of Mather’s average action and integrability on closed surfaces.

          Nonlinearity 24 (6): 1777 - 1793, 2011.

[7]     Leo T. Butler and Alfonso Sorrentino.

          Weak Liouville-Arnol’d theorems and their implications.

          Comm. Math. Phys. 315 (1): 109 - 133, 2012.

[8]     Alfonso Sorrentino.

          A variational approach to the study of the existence of invariant Lagrangian graphs.

          Boll. Unione Mat. Italiana Serie IX, Vol VI (2): 405 - 440, 2013.

[9]     Gabriel P. Paternain and Alfonso Sorrentino.

          Symplectic and contact properties  Mañé's critical value on the universal cover.

          Nonlinear Differential Equations Appl. (NoDEA) 21(5): 679 - 708, 2014.

[10]     Alfonso Sorrentino.

          Computing Mather’s β-function for Birkhoff billiards.

          Discrete and Contin. Dyn. Syst.- A, 35 (10): 5055 - 5082, 2015.

[11]     Alfonso Sorrentino.

           Action-minimizing methods in Hamiltonian dynamics: an introduction to Aubry- Mather theory.

          Monograph in the Series: Mathematical Lecture Notes Vol. 50, Princeton University Press, 2015.

[12]     Alfonso Sorrentino.

          Lecture notes on Mather’s theory for Lagrangian systems.

          Publicationes Matemática del Uruguay,16: 169-192, 2016.

[13]     Marco Mazzuccheli and Alfonso Sorrentino.

          Remarks on the symplectic invariance of Aubry-Mather sets.

          C. R. Acad. Sci. Paris, Ser. I 354: 419-423, 2016.

[14]     Stefano Marò and Alfonso Sorrentino.

          Aubry-Mather theory for conformally symplectic systems.

          Comm. Math. Phys., 354 (2): 775-808, 2017.

[15]     Antonio Siconolfi and Alfonso Sorrentino.

          Global results for Eikonal Hamilton-Jacobi equations on networks.

          Analysis & PDE, 11 (1): 171-211, 2018.

[16]     Guan Huang, Vadim Kaloshin and Alfonso Sorrentino.

          On Marked Length Spetrum of Generic Strictly Convex Billiard Tables.

          Duke Math. Journal, 167 (1): 175 - 209, 2018.

[17]     Guan Huang, Vadim Kaloshin and Alfonso Sorrentino.

          Nearly circular domains which are integrable close to the boundary are ellipses.

          Geom. and Funct. Analysis (GAFA), 28 (2): 334-392, 2018.

[18]     Vadim Kaloshin and Alfonso Sorrentino.

          On the local Birkhoff conjecture for convex billiards.

          Annals of Mathematics, 188 (1): 315-380, 2018.

[19]     Vadim Kaloshin and Alfonso Sorrentino.

          On the integrability of Birkhoff billiards.

          Philosophical Transactions of the Royal Society A, Volume 376, Issue 2131, 2018.

[20]     Alfonso Sorrentino.

          I matematici giocano... a biliardo (In Italian)

          Matematica, Cultura e Società, Rivista dell’Unione Matematica Italiana, Serie I, vol. 4, N.2, 2019.

[21]     Alfonso Sorrentino and Alexander P. Veselov.

          Markov numbers, Mather’s beta function and stable norm.

          Nonlinearity, 32 (6): 2147 - 2156, 2019.

[22]     Alfonso Sorrentino.

          On John Mather’s seminal contributions in Hamiltonian dynamics.

          Methods and Applications of Analysis (Issue in memory of John N. Mather), 26 (1): 37-64, 2019.

[23]      Alfonso Sorrentino.

          On the integrability of Birkhoff billiards.

          Oberwolfach report, European Mathematical Society Publishing, 16 (3): 1861-1863, 2019.

[24]     Vadim Kaloshin and Alfonso Sorrentino.

          Inverse problems and rigidity questions in billiard dynamics.

          Ergodic theory and Dynamical Systems (Issue in memory of A. Katok), 42 (03): 1023-1056, 2022

[25] Carlo Carminati, Stefano Marmi, David Sauzin and Alfonso Sorrentino.

          On the regularity of Mather's β-function for standard-like twist maps.

          Advances in Mathematics, 377: 107460,2021.  

[26]  Stefano Galatolo and Alfonso Sorrentino.

          Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms

          of  the circle  

          Discrete and Continuous Dynamical Systems, Series A, 42 (2): 815-839, 2022.

[27]  Marie-Claude Arnaud, Jessica Massetti and Alfonso Sorrentino.

          On the fragility of periodic tori for families of symplectic twist maps.

           Advances in Mathematics, 429: 109175, 2023.

[28]  Antonio Siconolfi and Alfonso Sorrentino.

          Aubry-Mather theory on graphs.

           Nonlinearity 36 (11): 5819, 2023.

[29]  Alfonso Sorrentino.

          On the fragility of periodic tori for families of symplectic twist maps.

          Oberwolfach report, European Mathematical Society Publishing, 20 (3), 2023.

[30]  Corentin Fierobe, Vadim Kaloshin, Alfonso Sorrentino.     

          Lecture notes on Birkhoff billiards: dynamics, integrability and spectral rigidity.

          Modern aspects of dynamical systems (Cetraro, Italy, 2021).  

          Lecture notes in Mathematics Vol. 2347, Springer, pp. 1-58, 2024

[31]  Corentin Fierobe,  Alfonso Sorrentino.     

          On the existence of periodic invariant curves for analytic families of twist maps and billiards.

          Revista Matemática Iberoamericana, Onlinefirst 2025. ArXiv: 2407.1790, 2024.

[32]      Corentin Fierobe, Alfonso Sorrentino, Amir Vig.

          Deformational Spectral rigidity of axially-symmetric symplectic billiards.

          Nonlinearity 38 (10): 105010, 2025.

     Preprints

•     Anna Florio, Martin Leguil, Alfonso Sorrentino.     

          On the rigidity of the stable norm and Mather's beta function of geodesic flows, 2025

•     Stefano Baranzini, Misha Bialy, Alfonso Sorrentino.

          Isoperimetric-type inequalities for Mather's beta function of convex billiards.

          ArXiv: 2509.06915, 2025.

•     Marco Pozza, Alfonso Sorrentino.     

          Stochastic Homogenization of  the Hamilton-Jacobi equations on manifolds.

          ArXiv: 2510.11714, 2025.

•     Alfonso Sorrentino, Lin Wang.     

          On the destruction of invariant Lagrangian graphs for conformal symplectic twist maps.

          ArXiv: 2504.06773, 2025.

•     Marco Pozza, Antonio Siconolfi,  Alfonso Sorrentino.     

          Homogenization of  Hamilton-Jacobi equations on networks.

          ArXiv: 2411.03803, 2024.

•     Rafael Ruggiero,  Alfonso Sorrentino.     

          On the set of asymptotic homologies of orbits on invariant Lagrangian graphs.

          ArXiv: 2409.16010, 2024.

•     Alfonso Sorrentino.

          Homogenization of the Hamilton-Jacobi equation.

          ArXiv: 1904.01359, 2015 (revised 2019).

Research

Publications

(see also ArXiv)