Publications

  1. Berti, M. and Maspero, A., Long time dynamics of Schrödinger and wave equations on flat tori, J. Differential Equations, vol. 267, n. 2, pp. 1167-1200, 2019.
  2. Berti, Massimiliano, KAM theory for partial differential equations Anal. Theory Appl., vol. 35, n. 3, pp. 235-267, 2019.
  3. Baldi, Pietro and Berti, Massimiliano and Haus, Emanuele and Montalto, Riccardo, KAM for gravity water waves in finite depth, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., vol. 29, n. 2, pp. 215-236, 2018.
  4. Baldi, Pietro and Berti, Massimiliano and Haus, Emanuele and Montalto, Riccardo, Time quasi-periodic gravity water waves in finite depth, Invent. Math., vol. 214, n. 2, pp. 739-911, 2018.
  5. Berti, Massimiliano and Kappeler, Thomas and Montalto, Riccardo, Large KAM tori for perturbations of the defocusing NLS equation Astérisque, n. 403, pp. viii+148, 2018.
  6. Berti, Massimiliano and Montalto, Riccardo, Quasi-periodic water waves, J. Fixed Point Theory Appl., vol. 19, n. 1, pp. 129-156, 2017.
  7. Baldi, Pietro and Berti, Massimiliano and Montalto, Riccardo, KAM for autonomous quasi-linear perturbations of KdV, Boll. Unione Mat. Ital., vol. 9, n. 2, pp. 143-188, 2016.
  8. Baldi, Pietro and Berti, Massimiliano and Montalto, Riccardo, KAM for autonomous quasi-linear perturbations of KdV, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 33, n. 6, pp. 1589-1638, 2016.
  9. Berti, Massimiliano, KAM for PDEs, Boll. Unione Mat. Ital., vol. 9, n. 2, pp. 115-142, 2016.
  10. Berti, Massimiliano and Corsi, Livia and Procesi, Michela, An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds, Comm. Math. Phys., vol. 334, n. 3, pp. 1413-1454, 2015.
  11. Baldi, Pietro and Berti, Massimiliano and Montalto, Riccardo, KAM for quasi-linear KdV, C. R. Math. Acad. Sci. Paris, vol. 352, n. 7-8, pp. 603-607, 2014.
  12. Baldi, Pietro and Berti, Massimiliano and Montalto, Riccardo, KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation, Math. Ann., vol. 359, n. 1-2, pp. 471-536, 2014.
  13. Berti, Massimiliano and Biasco, Luca and Procesi, Michela, KAM for reversible derivative wave equations, Arch. Ration. Mech. Anal., vol. 212, n. 3, pp. 905-955, 2014.
  14. Baldi, Pietro and Berti, Massimiliano and Montalto, Riccardo, A "NOTE" on KAM theory for quasi-linear and fully nonlinear forced KdV, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., vol. 24, n. 3, pp. 437-450, 2013.
  15. Berti, Massimiliano and Biasco, Luca and Procesi, Michela, Existence and stability of quasi-periodic solutions for derivative wave equations, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., vol. 24, n. 2, pp. 199-214, 2013.
  16. Berti, Massimiliano and Biasco, Luca and Procesi, Michela, KAM theory for the Hamiltonian derivative wave equation, Ann. Sci. éc. Norm. Supér. (4), vol. 46, n. 2, pp. 301-373 (2013), 2013.
  17. Berti, Massimiliano and Bolle, Philippe, Quasi-periodic solutions with Sobolev regularity of NLS on $Bbb T^d$ with a multiplicative potential, J. Eur. Math. Soc. (JEMS), vol. 15, n. 1, pp. 229-286, 2013.
  18. Berti, Massimiliano and Bolle, Philippe, Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential, Nonlinearity, vol. 25, n. 9, pp. 2579-2613, 2012.
  19. Bambusi, D. and Berti, M. and Magistrelli, E., Degenerate KAM theory for partial differential equations, J. Differential Equations, vol. 250, n. 8, pp. 3379-3397, 2011.
  20. Berti, Massimiliano and Biasco, Luca, Branching of Cantor manifolds of elliptic tori and applications to PDEs, Comm. Math. Phys., vol. 305, n. 3, pp. 741-796, 2011.
  21. Berti, Massimiliano and Bolle, Philippe, Quasi-periodic solutions of nonlinear Schrödinger equations on $Bbb T^d$, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., vol. 22, n. 2, pp. 223-236, 2011.
  22. Berti, Massimiliano and Procesi, Michela, Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces, Duke Math. J., vol. 159, n. 3, pp. 479-538, 2011.
  23. Berti, M. and Bolle, P. and Procesi, M., An abstract Nash-Moser theorem with parameters and applications to PDEs, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 27, n. 1, pp. 377-399, 2010.
  24. Berti, Massimiliano and Bolle, Philippe, Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions, Arch. Ration. Mech. Anal., vol. 195, n. 2, pp. 609-642, 2010.
  25. Baldi, Pietro and Berti, Massimiliano, Forced vibrations of a nonhomogeneous string, SIAM J. Math. Anal., vol. 40, n. 1, pp. 382-412, 2008.
  26. Berti, Massimiliano and Bolle, Philippe, Cantor families of periodic solutions of wave equations with $C^k$ nonlinearities, NoDEA Nonlinear Differential Equations Appl., vol. 15, n. 1-2, pp. 247-276, 2008.
  27. Berti, Massimiliano and Bolle, Philippe, Cantor families of periodic solutions for completely resonant wave equations, Front. Math. China, vol. 3, n. 2, pp. 151-165, 2008.
  28. Berti, Massimiliano and Bolle, Philippe, Cantor families of periodic solutions for wave equations via a variational principle, Adv. Math., vol. 217, n. 4, pp. 1671-1727, 2008.
  29. Berti, Massimiliano and Matzeu, Michele and Valdinoci, Enrico, On periodic elliptic equations with gradient dependence, Commun. Pure Appl. Anal., vol. 7, n. 3, pp. 601-615, 2008.
  30. Baldi, Pietro and Berti, Massimiliano, Periodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., vol. 17, n. 3, pp. 257-277, 2006.
  31. Berti, Massimiliano and Procesi, Michela, Quasi-periodic solutions of completely resonant forced wave equations, Comm. Partial Differential Equations, vol. 31, n. 4-6, pp. 959-985, 2006.
  32. Berti, Massimiliano and Bolle, Philippe, Cantor families of periodic solutions for completely resonant nonlinear wave equations, Duke Math. J., vol. 134, n. 2, pp. 359-419, 2006.
  33. Berti, Massimiliano and Biasco, Luca, Forced vibrations of wave equations with non-monotone nonlinearities, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 23, n. 4, pp. 439-474, 2006.
  34. Bambusi, Dario and Berti, Massimiliano, A Birkhoff-Lewis-type theorem for some Hamiltonian PDEs, SIAM J. Math. Anal., vol. 37, n. 1, pp. 83-102, 2005.
  35. Berti, Massimiliano and Biasco, Luca, Periodic solutions of nonlinear wave equations with non-monotone forcing terms Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., vol. 16, n. 2, pp. 117-124, 2005.
  36. Berti, Massimiliano and Procesi, Michela, Quasi-periodic oscillations for wave equations under periodic forcing Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., vol. 16, n. 2, pp. 109-116, 2005.
  37. Berti, Massimiliano and Bolle, Philippe, Bifurcation of free vibrations for completely resonant wave equations Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), vol. 7, n. 2, pp. 519-528, 2004.
  38. Berti, Massimiliano and Bolle, Philippe, Multiplicity of periodic solutions of nonlinear wave equations, Nonlinear Anal., vol. 56, n. 7, pp. 1011-1046, 2004.
  39. Berti, Massimiliano and Biasco, Luca and Valdinoci, Enrico, Periodic orbits close to elliptic tori and applications to the three-body problem Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), vol. 3, n. 1, pp. 87-138, 2004.
  40. Berti, Massimiliano, Periodic solutions of Hamiltonian PDEs Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), vol. 7, n. 3, pp. 647-661, 2004.
  41. Berti, Massimiliano and Biasco, Luca and Bolle, Philippe, Drift in phase space: a new variational mechanism with optimal diffusion time, J. Math. Pures Appl. (9), vol. 82, n. 6, pp. 613-664, 2003.
  42. Berti, Massimiliano and Bolle, Philippe, Periodic solutions of nonlinear wave equations with general nonlinearities, Comm. Math. Phys., vol. 243, n. 2, pp. 315-328, 2003.
  43. Berti, Massimiliano and Biasco, Luca and Bolle, Philippe, Optimal stability and instability results for a class of nearly integrable Hamiltonian systems Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., vol. 13, n. 2, pp. 77-84, 2002.
  44. Berti, Massimiliano and Bolle, Philippe, Fast Arnold diffusion in systems with three time scales, Discrete Contin. Dyn. Syst., vol. 8, n. 3, pp. 795-811, 2002.
  45. Berti, Massimiliano and Carminati, Carlo, Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems, Nonlinear Anal., vol. 48, n. 4, Ser. A: Theory Methods, pp. 481-504, 2002.
  46. Berti, Massimiliano and Bolle, Philippe, A functional analysis approach to Arnold diffusion, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 19, n. 4, pp. 395-450, 2002.
  47. Berti, Massimiliano and Malchiodi, Andrea, Non-compactness and multiplicity results for the Yamabe problem on $S^n$, J. Funct. Anal., vol. 180, n. 1, pp. 210-241, 2001.
  48. Berti, Massimiliano and Bolle, Philippe, Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., vol. 11, n. 4, pp. 235-243 (2001), 2000.
  49. Berti, Massimiliano and Bolle, Philippe, Homoclinics and chaotic behaviour for perturbed second order systems, Ann. Mat. Pura Appl. (4), vol. 176, pp. 323-378, 1999.
  50. Ambrosetti, Antonio and Berti, Massimiliano, Homoclinics and complex dynamics in slowly oscillating systems, Discrete Contin. Dynam. Systems, vol. 4, n. 3, pp. 393-403, 1998.
  51. Berti, Massimiliano and Bolle, Philippe, Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., vol. 9, n. 3, pp. 167-175, 1998.
  52. Berti, Massimiliano and Bolle, Philippe, Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), vol. 27, n. 2, pp. 331-377 (1999), 1998.
  53. Berti, Massimiliano, Heteroclinic solutions for perturbed second order systems Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., vol. 8, n. 4, pp. 251-262, 1997.
  54. Berti, Massimiliano, Some remarks on a variational approach to Arnold's diffusion, Discrete Contin. Dynam. Systems, vol. 2, n. 3, pp. 307-314, 1996.

Preprints

  1. Berti, Massimiliano, KAM theory for prova Anal. Theory Appl., vol. 35, n. 3, pp. 235-267, 2019.

Books

  1. Berti, Massimiliano and Delort, Jean-Marc, Almost global solutions of capillary-gravity water waves equations on the circle, Springer, Cham; Unione Matematica Italiana, [Bologna], vol. 24, pp. x+268, 2018.
  2. Berti, Massimiliano, Variational methods for Hamiltonian PDEs, Hamiltonian dynamical systems and applications, Springer, Dordrecht, pp. 391-420, 2008.
  3. Berti, Massimiliano, Nonlinear oscillations of Hamiltonian PDEs Birkhäuser Boston, Inc., Boston, MA, vol. 74, pp. xiv+180, 2007.

Proceedings

  1. Berti, Massimiliano and Bolle, Philippe, A Nash-Moser approach to KAM theory, Hamiltonian partial differential equations and applications, Fields Inst. Res. Math. Sci., Toronto, ON, vol. 75, pp. 255-284, 2015.
  2. Berti, Massimiliano, Quasi-periodic solutions of PDEs Séminaire Laurent Schwartz-équations aux dérivées partielles et applications. Année 2011-2012, école Polytech., Palaiseau, pp. Exp. No. XXX, 11, 2013.
  3. Berti, Massimiliano, Nonlinear vibrations of completely resonant wave equations, Fixed point theory and its applications, Polish Acad. Sci. Inst. Math., Warsaw, vol. 77, pp. 49-60, 2007.
  4. Berti, Massimiliano, Arnold diffusion: a functional analysis approach Symmetry in nonlinear mathematical physics, Part 1, 2(Kyiv, 2001), Natsional. Akad. Nauk Ukraini, Inst. Mat., Kiev, vol. 2, pp. 712-719, 2002.
  5. Berti, Massimiliano, A functional analysis approach to Arnold diffusion, Symmetry and perturbation theory (Cala Gonone, 2001), World Sci. Publ., River Edge, NJ, pp. 29-31, 2001.
  6. Ambrosetti, A. and Berti, M., Applications of critical point theory to homoclinics and complex dynamics Discrete Contin. Dynam. Systems, n. Added "VOLUME" I, pp. 72-78, 1998.