M. Berti, P. Bolle, “Quasi-periodic solutions of nonlinear wave equations on T^d”, vii + 355, Monographs of the EMS, 2020, doi 10.4171/211 ISBN print 978-3-03719-211-5.
M. Berti, J-M. Delort, “Almost global solutions for capillarity-gravity water waves equations on the circle”, UMI Lecture Notes, 24, x+268 pages, 2018. Monograph awarded for the UMI book prize 2017. ISBN 978-3-319-99485-7
M. Berti, “Nonlinear Oscillations of Hamiltonian PDEs”, Progress in Nonlinear Differential Equations, Birkhauser, 1-180 pages, Boston, 2008. book/10.1007/978-0-8176-4681-3
M. Berti, L. Corsi, A. Maspero, P. Ventura, “Infinitely many isolas of modulational instability for Stokes waves”, preprint arXiv:2405.05854
M. Berti, R. Feola, M. Procesi, S. Terracina, "Reducibility of Klein-Gordon equations with maximal order perturbations", preprint arXiv:2402.11377 to appear in Memoires EMS
M. Berti, A. Maspero, P. Ventura, "First isola of modulational instability of Stokes waves in deep water", preprint arXiv:2402.11377, to appear EMS Surveys in Mathematical Sciences
M. Berti, S. Cuccagna, F. Gancedo, S. Scrobogna, "Paralinearization and extended lifespan for solutions of the \alpha-SQG sharp front equation", Advances in Math. 460, 2025 arXiv:2310.15963
M. Berti, B. Langella, D. Silimbani, ``Time periodic solutions of completely resonant Klein-Gordon equations on S^3", Annales de l'Institute Henry Poincaré, DOI 10.4171/AIHPC/125, 2024.
L. Asselle, G. Benedetti, M. Berti, ``Zoll magnetic systems on the two-torus: a Nash-Moser construction", https://arxiv.org/abs/2304.02765. Advances in Math, 452 2024https://doi.org/10.1016/j.aim.2024.10982
M. Berti, A. Maspero, F. Murgante, ``Hamiltonian Birkhoff normal form for gravity-capillary water waves with constant vorticity: almost global existence", Annals of PDEs, 10, 22, 2024. https://doi.org/10.1007/s40818- 024-00182-z
M. Berti, L. Franzoi, A. Maspero, “Pure gravity traveling quasi-periodic water waves with constant vorticity”, arxiv 2101.12006 Communications Pure Applied Mathematics, Volume77, Issue 2, 990-1064, 2024, doi 10.1002/cpa.22143.
M. Berti, A. Maspero, P. Ventura, ``Stokes waves at the critical depth are modulational unstable", Comm. Math. Phys., 405-56, 2024.
M. Berti, A. Maspero, P. Ventura, “Benjamin-Feir instability of Stokes waves in finite depth”, Archive Rational Mechanics, 247, 91, 2023, https://doi.org/10.1007/s00205-023-01916-2.
M. Berti, Z. Hassaina, N. Masmoudi, "Time quasi-periodic vortex patches", Inventiones Mathematicae, 233, 1279-1391, 2023
M. Berti, A. Maspero, P. Ventura, “On the analyticity of the Dirichlet- Neumann operator and Stokes waves”, Rendiconti Lincei Matematica e Applicazioni, 33, 611-650, 2022, doi 10.4171/RLM/983
M. Berti, A. Maspero, P. Ventura, “Full description of Benjamin-Feir instability of Stokes waves in deep water”, Inventiones Mathematicae. doi.org/10.1007/s00222-022-01130-z, 230, no. 2, 651--711, 2022.
M. Berti, R. Feola, F. Pusateri, “Birkhoff normal form and long time existence for periodic gravity water waves”, Communications Pure Applied Mathematics, doi/10.1002/cpa.22041, Volume76, Issue7, Pages 1416-1494, 2023.
M. Berti, T. Kappeler, R. Montalto, “Large KAM tori for quasi-linear perturbations of KdV”, Archive Rational Mechanics, 239, 1395-1500, doi.org/10.1007/s00205-020-01596-2, 2021.
M. Berti, A. Maspero, F. Murgante, “Local well posedness of the Euler-Korteweg equations on T^d”, Journal of Dynamics and Differential Equations, https://doi.org/10.1007/s10884-020-09927-3, 2021.
M. Berti, L. Franzoi, A. Maspero, “Traveling quasi-periodic water waves with constant vorticity”, Archive Rational Mechanics, 240, 99-202, 2021. 10.1007/s00205-021-01607-w
M. Berti, R. Montalto, “KAM for gravity capillary water waves”, Memoires American Mathematical Society, Volume 263, 1273, ISSN 0065-9266, 2020.
M. Berti, R. Feola, F. Pusateri, “Birkhoff normal form for gravity water waves”, https://doi.org/10.1007/s42286-020-00024-y Water Waves, 2020.
M. Berti, R. Feola, L. Franzoi, “Quadratic life span of periodic gravity-capillary water waves”, https://doi.org/10.1007/s42286-020-00036-8 Water Waves, 2020.
M. Berti, “KAM theory for partial differential equations”, Analysis in Theory and Applications, 35, no. 3, 235–267, 2019.
M. Berti, A. Maspero, “Long time dynamics of Schrodinger and wave equations on flat tori”, Journal Differential Equations, 267, no. 2, 1167– 1200, 2019.
M. Berti, T. Kappeler, R. Montalto, “Large KAM tori for perturbations of the dNLS equation”, Asterisque, 403, viii+148, 2018. ISBN 978-2-85629-892-3
P. Baldi, M. Berti, E. Haus, R. Montalto, “KAM for gravity water waves in finite depth”, Rendiconti Lincei Matematica e Applicazioni, n. 2, 215-236, 29, 2018.
P. Baldi, M. Berti, E. Haus, R. Montalto, “Time quasi-periodic gravity water waves in finite depth”, Inventiones Mathematicae, 214, 739–911, 2018.
M. Berti, R. Montalto, “Quasi-periodic water waves”, Journal Fixed Point Theory Applications, Volume 19, Issue 1, pp 129–156, 2017.
P. Baldi, M. Berti, R. Montalto, “KAM for autonomous quasi-linear perturbations of KdV”, Annales I.H. Poincaré , analyse nonlineaire, 33, 1589-1638, 2016.
P. Baldi, M. Berti, R. Montalto, “KAM for autonomous quasi-linear perturbations of mKdV”, Bollettino Unione Matematica Italiana, 9, no. 2, 143-188, 2016.
M. Berti, “KAM for PDEs”, Bollettino Unione Matematica Italiana, 9, no. 2, 115-142, 2016.
M. Berti, L. Corsi , M. Procesi, “An abstract Nash-Moser theorem and quasi- periodic solutions for NLW and NLS on compact Lie groups and homogeneous spaces”, Communication in Mathematical Physics, 334, no. 3, 1413- 1454, 2015.
Berti M., Bolle P., "A Nash-Moser approach to KAM theory", Field Institute Communications, 255-284, special volume ‘Hamiltonian PDEs and Applications”, 2015.
M. Berti, L. Biasco, M. Procesi, “KAM for reversible derivative wave equations”, Archive Rational Mechanics and Analysis, 212, 905-955, 2014.
P. Baldi, M. Berti, R. Montalto “KAM theory for quasi-linear and fully nonlinear forced perturbations of Airy equations”, Mathematische Annalen, 359, 1, 471-536, 2014.
P. Baldi, M. Berti, R. Montalto “KAM for quasi-linear KdV”, Comptes rendus Mathematique Acad. Sci., Ser. I 352, 603-607, 2014.
M. Berti, P. Bolle, “Quasi-periodic solutions with Sobolev regularity of NLS on T^d and a multiplicative potential”, Journal European Mathematical Society, 15, 229-286, 2013.
M. Berti, L. Biasco, M. Procesi, “Existence and stability of quasi-periodic solutions for derivative wave equations”, Rend. Lincei Mat. Appl., 24, 1-16, 2013.
M. Berti, L. Biasco, M. Procesi, “KAM theory for the Hamiltonian derivative wave equation”, Annales Scientifiques de l’ Ecole Normale Superieure, Volume 46, fascicule 2, p. 299-371, 2013.
P. Baldi, M. Berti, R. Montalto, “A note on KAM theory for quasi-linear and fully nonlinear KdV”, Rend. Lincei Mat. Appl. 24, 437-450, 2013.
M. Berti, P. Bolle, “Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential”, Nonlinearity, 25, 2579-2613, 2012.
M. Berti, M.Procesi, “Nonlinear wave and Schrodinger equations on compact Lie groups and homogeneous spaces”, Duke Mathematical Journal, 159, 3, 479-538, 2011.
M. Berti, L. Biasco, “Branching of Cantor manifolds of elliptic tori and applications to PDEs”, Communications in Mathematical Physics, 305, 3, 741-796, 2011.
M. Berti, P. Bolle, “Quasi-periodic solutions of NLS on T^d” Rend. Mat. Acc. Naz. Lincei, 22, 223-236, 2011.
D. Bambusi, M. Berti, E. Magistrelli, “Degenerate KAM theory for partial differential equations”, Journal Differential Equations, 250, 3379-3397, 2011.
M. Berti, P. Bolle, “Sobolev Periodic solutions for nonlinear wave equations in higher spatial dimensions”, Archive for Rational Mechanics and Analysis, 195, 609-642, 2010.
M. Berti, P. Bolle, M.Procesi, “An abstract Nash-Moser theorem with parameters and applications to PDEs”, Annales de l’Institute Henry Poincaré, Analyse non lineaire, 27, 377 - 399, 2010.
M. Berti, P. Bolle, “Cantor familites of periodic solutions for wave equations via a variational principle”, Advances in Mathematics, 217, 1671-1727, 2008.
P. Baldi, M. Berti, “Forced vibrations of a nonhomogeneous string”, SIAM Journal in Mathematical Analysis, 40, 1, 382-412, 2008.
M. Berti, M. Matzeu, E. Valdinoci, “On periodic elliptic equations with gradient dependence”, Communications in Pure and Applied Analysis, 601-615, 7, 3, 2008.
M. Berti, P. Bolle, “Cantor families of periodic solutions of wave equations with C^k nonlinearities”, Nonlinear Differential Equations and Applications, 15, 247-276, 2008.
M. Berti, Lectures on “Variational Methods for Hamiltonian PDEs”, Nato summer School “Hamiltonian Dynamical Systems and Applications”, Montreal 391-420, chapter, Springer, W. Craig editor, 2007.
M. Berti, P. Bolle, “Cantor families of periodic solutions for completely resonant nonlinear wave equations”, Duke Mathematical Journal, 134, issue 2, 359-419, 2006.
M. Berti, L. Biasco: “Forced vibrations of wave equations with non-monotone nonlinearities”, Annales de l’Institute H. Poincaré, Analyse non lineaire, Vol. 23, issue 4, 2006, 439-474.
M. Berti, M. Procesi: “Quasi-periodic solutions of completely resonant forced wave equations”, Communications in Partial Differential Equation, 31, 6, 959-985, 2006.
P. Baldi, M. Berti, “Periodic solutions of wave equations for asympotically full measure sets of frequencies”, Rend. Mat. Acc. Naz. Lincei, Volume 17, Issue 3, 257-277, 2006.
D. Bambusi, M. Berti: “A Birkhoff-Lewis type theorem for some Hamiltonian PDEs”, SIAM Journal on Mathematical Analysis, 37, 1, 83-102, 2005.
M. Berti, L. Biasco: "Periodic solutions of nonlinear wave equations with non- monotone forcing terms", Rend. Mat. Acc. Naz. Lincei, s. 9, v. 16, fasc. 2, 117-124, 2005.
M. Berti, M. Procesi: “Quasi-periodic oscillations for wave equations under periodic forcing”, Rend. Mat. Acc. Naz. Lincei, 9, 16, 2, 109-116, 2005.
M. Berti, P. Bolle: “Multiplicity of periodic solutions of nonlinear wave equations”, Nonlinear Analysis, Theory Methods Applications, 56/7, pp. 1011-1046, 2004.
M. Berti, L. Biasco, E. Valdinoci: “Periodic orbits close to elliptic tori and applications to the three-body problem”, Annali Scuola Normale Superiore di Pisa, Cl. Sci. (V) 3, 87-138, 2004.
M. Berti, P. Bolle: “Bifurcation of free vibrations for completely resonant wave equations”, Bolletino Unione Mat. Italiana, 7, 2, 2004.
M. Berti, P. Bolle: “Periodic solutions of nonlinear wave equations with general nonlinearities”, Communications in Mathematical Physics, Vol. 243, 2, pp. 315-328, 2003.
M. Berti, L. Biasco, P. Bolle: “Drift in phase space: a new variational mechanism with optimal diffusion time”, Journal des Mathematiques Pures et Appliquées, 82/6, pp. 613-664, 2003.
M. Berti, L. Biasco, P. Bolle: “Optimal stability and instability results for a class of nearly integrable Hamiltonian systems”, Rend. Mat. Acc. Naz. Lincei, s. 9, vol. 13, fasc. 2, pp. 77-84, 2002.
M. Berti, P. Bolle: “A functional analysis approach to Arnold Diffusion”, Annales de l’Institute Henry Poincaré, Analyse non lineaire, 19, 4, 395-450, 2002.
M. Berti, P. Bolle: “Fast Arnold diffusion in systems with three time scales”, Discrete and Continuous Dynamical Systems, series A, Vol. 8, n. 3, pp. 795-811, 2002.
M. Berti, C. Carminati: “Chaotic dynamics for perturbations of infinite dimensional Hamiltonian systems”, Nonlinear Analysis TMA, 48, pp. 481- 504, 2002.
M. Berti, A. Malchiodi: “Non-compactenss and multiplicity results for the Yamabe problem on S^n”, Journal of Functional Analysis, vol. 180, n.1 febbraio 2001.
M. Berti, P. Bolle: “Variational construction of Homoclinics and Chaotic Be- haviour in presence of a saddle-saddle equilibrium”, Annali Scuola Normale Superiore di Pisa, serie IV, vol. XXVII, fasc. 2, 1998.
M. Berti: “Heteroclinic solutions for perturbed second order systems”, Rend. Mat. Acc. Naz. Lincei, s. 9, vol. 8, fasc.4, 1998.
M. Berti, P. Bolle: “Homoclinics and Chaotic Behaviour for Perturbed Second order Systems”, Annali di Matematica Pura e Applicata, vol. CLXXVI, pp. 323-378, 1999.
A. Ambrosetti, M. Berti: “Homoclinics and Complex dynamics in slowly oscillating systems”, Discrete and Continuous dynamical systems, vol. 4, n.3, 1998.
M. Berti: “Some remarks on a variational approach to Arnold diffusion”, Discrete and Continuous dynamical systems, vol. 2, n. 3, 1996.
M. Berti, P. Bolle: “Variational construction of Homoclinics and Chaotic Behaviour in presence of a saddle-saddle equilibrium”, Rend. Mat. Acc. Naz. Lincei, s. 9, vol. 9, fasc. 3, 1998.
M. Berti, ``KAM for vortex patches", Regular and Chaotic Dynamics, 2024, https://doi.org/10.1134/S1560354724540013.
``Stable and unstable Stokes waves", Séminaire Laurent-Schwartz EDP et applications Institut des hautes études scientifiques, 2024 Exposé no XIX.
M. Berti, A. Maspero, F. Murgante, "Hamiltonian paradifferential Birkhoff normal form for water waves", Regular and Chaotic Dynamics, Vol. 28, Nos. 4-5, pp. 543-560, 2023
M. Berti, “Stable and unstable periodic water waves”, Oberwolfach reports. Deterministic Dynamics and Randomness in PDE, 2022
M. Berti, A. Maspero, P. Ventura, “Benjamin-Feir instability of Stokes waves”, Rendiconti Lincei Matematica e Applicazioni
M. Berti. “KAM for water waves”, Oberwolfach reports. Dynamische Systeme, 2015
M. Berti. “KAM for quasi-linear KdV equations”, Oberwolfach reports. Dynamische Systeme, 10, 3, 2013
M. Berti “Quasi-periodic solutions of PDEs”, Seminaire Laurent Schwartz, IHES, 2012
M. Berti “Quasi periodic solutions of Hamiltonian PDEs”, 38-Journeé equations aux derivées partielles, Biarritz, 2011
M. Berti, P. Bolle: “Cantor families of periodic solutions in wave equations”, Frontiers Math. China, 3, 2008, 2, 151-165. ISSN: 2167-5163
M. Berti: “Nonlinear oscillations of completely resonant wave equations” for “Fixed point theory and Applications”, 49-60, Banach Center Publ. 77, Polish Acad. Sci. Warsaw, 2007 ISSN: 2167-5163
M. Berti: “Nonlinear oscillations of Hamiltonian PDEs”, Proceedings of Contributed talks Equadiff.11, Bratislava, 2005, 9-16, ISBN 978-80-227-2624-5
M. Berti: “Soluzioni periodiche di PDEs Hamiltoniane”, XVII Congresso UMI, Milano, Bolletino Unione Matematica Italiana, 8, 7-B, pp. 647-661, 2004. ISSN: 0392-4041
M. Berti: “Arnold diffusion: a functional analysis approach”, Proc. of Institute of Mathematics of Nas of Ukraine, Vol. 43, Part 2, 712-719, 2002. ISSN: 2167-5163
M. Berti: “A functional analysis approach to Arnold diffusion”, Proc. of the International conference SPT2001, World Scientific
M. Berti, P. Bolle: “Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems”, Rend. Mat. Acc. Naz. Lincei, s. 9, 11, 4, 235-243, 2000
A. Ambrosetti, M. Berti: “Applications of Critical Point Theory to Homoclinics and Complex Dynamics”, Discrete and Continuous Dynamical systems, Added Vol. I, 72-78, 1998