Pubblicazioni e Preprints

[1] M. Berti, "Some remarks on a variational approach to Arnold diffusion", Discrete and Continuous Dynamical Systems, vol. 2, n.3, 1996.

[2] A. Ambrosetti, M. Berti, "Homoclinics and Complex dynamics in slowly oscillating systems , Discrete and Continuous Dynamical Systems, vol. 4, n.3, 1998.

[3] M. Berti, "Heteroclinic solutions for perturbed second order systems" , Rend. Mat. Acc. Naz. Lincei , s. 9, vol. 8, fasc.4, 1998.

[4] M. Berti, P. Bolle, "Variational construction of Homoclinics and Chaos in presence of a saddle-saddle equilibrium", Annali Scuola Normale Superiore di Pisa, serie IV,vol. XXVII, fasc. 2, 1998. pdf

[5] M. Berti, P. Bolle, "Variational construction of Homoclinics and Chaos in presence of a saddle-saddle equilibrium", Rend. Mat. Acc. Naz. Lincei, s. 9, vol. 9, fasc. 3, 1998.

[6] 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. pdf

[7] M. Berti, P. Bolle, "Diffusion time and splitting of the separatrices in nearly integrable isochronous Hamiltonian systems", Rend. Mat. Acc. Naz. Lincei , s.9, vol. 11, fasc. 4, pp. 235-243, 2000.

[8] M. Berti, A. Malchiodi, "Non-compactness and Multiplicity results for the Yamabe problem on S^n", Journal of Functional Analysis , Vol. 180, No. 1, 2001. pdf

[9] M. Berti, C. Carminati, "Chaotic dynamics for perturbations of infinite dimensional Hamiltonian systems", Nonlinear Analysis, Theory, Methods, Applications , 48, 481-504, 2002. pdf

[10] 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. pdf

[11] M. Berti, P. Bolle, "A functional analysis approach to Arnold Diffusion", Annales Institute Henri Poincare', Analyse non-lineaire , 19, 4, pp. 395-450 2002. pdf

[12] 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.

[13] M. Berti, L. Biasco, P. Bolle, "Drift in phase space: a new variational mechanism with optimal diffusion time", Journal de Mathematiques Pures et Appliquees , 82/6 pp. 613-664, 2003. pdf

[14] M. Berti, P. Bolle, "Periodic solutions of nonlinear wave equations with general nonlinearities", Communications in Mathematical Physics , 243, 2, pp.315-328, 2003. pdf

[15] M. Berti, P. Bolle, "Multiplicity of periodic solutions of nonlinear wave equations", Nonlinear Analysis, Theory, Methods, Applications , 56-7, pp. 1011-1049, 2004. pdf

[16] 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. pdf

[17] M. Berti, P. Bolle, "Bifurcation of free vibrations for completely resonant wave equations", Bollettino Unione Matematica Italiana , (8) 7-B, 519-528, 2004.

[18] D. Bambusi, M. Berti, "A Birkhoof-Lewis type theorem for some Hamiltonian PDE's", SIAM Journal on Mathematical Analysis , 37, 1, 83-102, 2005. pdf

[19] M. Berti, L. Biasco, "Periodic solutions of nonlinear wave equations with nonmonotone forcing terms", Rend. Mat. Acc. Naz. Lincei , s.9, v.16, fasc.2, 107-124, 2005.

[20] M. Berti, M. Procesi, "Quasi-periodic oscillations for wave equations with periodic forcing", Rend. Mat. Acc. Naz. Lincei , s.9, v. 16, f.2, 109-116, 2005.

[21] M. Berti, P. Bolle, "Cantor families of periodic solutions for completely resonant nonlinear wave equations", Duke Mathematical Journal , 134, issue 2, 359-419, 2006. pdf

[22] M. Berti, L. Biasco, "Forced vibrations of wave equations with non-monotone nonlinearities", Annales de l'Institute H. Poincare', Analyse nonlinaire , Vol. 23, issue 4, 439-474, 2006. pdf

[23] P. Baldi, M. Berti, "Periodic solutions of wave equations for asymptotically full measure set of frequencies", Rend. Mat. Acc. naz. Lincei , Volume 17, Issue 3, 257-277, 2006. pdf

[24] M. Berti, M. Procesi, "Quasi-periodic solutions of completely resonant forced wave equations", Communications in Partial Differential Equations , 31, 6, 959-985, 2006. pdf

[25] M. Berti, P. Bolle, "Cantor families of periodic solutions for wave equations via a variational principle'' , Advances in Mathematics, 217, 1671-1727, 2008. pdf

[26] P. Baldi, M. Berti, "Forced vibrations of a nonhomogeneous string" , SIAM Journal on Mathematical Analysis, 40, 1, 382-412, 2008. pdf

[27] M. Berti, M. Matzeu, E. Valdinoci, "On periodic elliptic equations with gradient dependence" , Communications in Pure and Applied Analysis , 7, 3, 601-615, 2008, pdf

[28] 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 pdf

[29] M. Berti, P. Bolle, "Sobolev Periodic solutions of nonlineae wave equations in higher spatial dimension" Archive for Rational Mechanics and Analysis , 195, 609-642, 2010. pdf

[30] M. Berti, P. Bolle, M. Procesi "An abstract Nash-Moser theorem with parameters and applications to PDEs" Annales de l'Institute H. Poincare', Analyse nonlinaire, 27, 377 - 399, 2010. pdf

[31] M. Berti, M. Procesi, "Nonlinear wave and Schrodinger equations on compact Lie groups and homogeneous spaces" Duke Math. J., 159, 3, 479-538, 2011. pdf

[32] M. Berti, L. Biasco, "Branching of Cantor manifolds of elliptic tori and applications to PDEs" Comm. Math. Phys., 305, 3, 741-796, 2011. pdf

[33] M. Berti, P. Bolle, "Quasi-periodic solutions of NLS on T^d" Rend. Mat. Acc. Naz. Lincei, 22, 223-236, 2011. pdf

[34] D. Bambusi, M. Berti, E. Magistrelli, "Degenerate KAM theory for partial differential equations" Journal Differential Equations, 250, 3379-3397, 2011. pdf

[35] M. Berti, P. Bolle, "Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential" , Nonlinearity, 25, 2579-2613, 2012, "featured article". pdf

[36] M. Berti, P. Bolle, "Quasi-periodic solutions with Sobolev regularity of NLS on T^d and a multiplicative potential" , J. European Math. Society, 15, 229-286, 2013. pdf

[37] M. Berti, L. Biasco, M. Procesi, "KAM theory for the Hamiltonian derivative wave equation" , Annales Scientifiques de l'ENS, Volume 46, fascicule 2, p. 299-371, (2013), pdf

[38] M. Berti, L. Biasco, M. Procesi, "Existence and stability of quasi-periodic solutions of reversible derivative wave equations" , Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 24 (2013), 1-16, pdf

[39] P. Baldi, M. Berti, R. Montalto, "A note on KAM theory for quasi-linear and fully nonlinear KdV" , Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl. 24 (2013), 437-450,

[40] M. Berti, L. Biasco, M. Procesi, "KAM for the reversible derivative wave equation" , Archive for Rational Mechanics and Analysis, 212, 905-955, 2014 pdf

[41] P. Baldi, M. Berti, R. Montalto, " KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation " , Math. Annalen, 359, 471-536, 2014 pdf

[42] 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" , to appear on Comm. Math. Phys. pdf

[43] P. Baldi, M. Berti, R. Montalto, " KAM for quasi-linear KdV" , Comptes Rendu Math. 352, 603-607, 2014 pdf

[44] P. Baldi, M. Berti, R. Montalto, " KAM for autonomous quasi-linear perturbations of KdV" , preprint 2014 pdf

[45] M. Berti, P. Bolle " KAM for autonomous quasi-linear perturbations of KdV" , to appear on Field Institute Communications, a volume in honour of Walter Craig. pdf

Book

M. Berti, Monografia. "Nonlinear Oscillations of Hamiltonian PDEs'', Progress in Nonlinear Differential Equations and Its Applications, 74, Birkhauser, Boston, 1-181, 2008.

M. Berti, capitolo. Lectures on "Variational Methods for Hamiltonian PDEs", Hamiltonian Dynamical systems and applications, 391-420, Springer, Dordrecht, Nato summer School "Hamiltonian Dynamical Systems and Applications", Montreal, 2007, ISSN: 2167-5163

Proceedings

[1] A. Ambrosetti, M.Berti, "Applications of Critical Point Theory to Homoclinics and Complex Dynamics", Proc. of the International Conference Dynamical Systems and Differential Equations, Discrete and Continuous Dyncamical systems, Added Vol. I, 72-78, W.Chen and S.Hu editors, 1998.

[2] M. Berti, "A Functional Analysis approach to Arnold Diffusion", Proc. of the International Conference SPT 2001, World scientific, Ed. D.Bambusi, G.Gaeta, M.Cadoni.

[3] 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

[4] M. Berti, "Soluzioni periodiche di PDEs Hamiltoniane", invited conference 30 m. at XVII Congresso UMI, Milano, 8-13 settembre 2003, Bollettino Unione Matematica Italiana 8, 7-B, pp. 647-661, 2004. ISSN: 0392-4041

[5] M. Berti, "Nonlinear vibrations of completely resonant wave equations", "Fixed point theory and Applications", 49-60, Banach Center Publ. 77, Polish Acad. Sci. Warsaw, 2007 ISSN: 2167-5163.

[6] M. Berti, "Nonlinear oscillations in wave equations", Proc. of Equadiff 11, pp. 916, invited conference by P. Rabinowitz, Bratislava, 2005. ISBN 978-80-227-2624-5

[7] M. Berti, P. Bolle "Cantor families of periodic solutions for completely resonant wave equations", Frontiers Math. China, 3, 2008, 2, 151-165. ISSN: 2167-5163

[8] M. Berti "Quasi periodic solutions of Hamiltonian PDEs", Journee' equations aux derive'es partielles, Biarritz 2011.

[9] M. Berti "Quasi periodic solutions of PDEs", Seminaire Laurent Schwartz, February 2012, F. Merle, F. Golse.

[10] M. Berti "KAM for quasi linear KdV equations", Oberwolfach reports, vol 10, edited by Eliasson, Hofer, Yoccoz, 1982-1985, 2013.

Some talks 2012-'13

[1] M.Berti, "Quasi-periodic solutions of PDEs ", St. Etienne, January, 2012.

[2] M.Berti, "Quasi-periodic solutions of PDEs ", IHES, February, 2012.

[3] M.Berti, "New connections between dynamical systems and Hamiltonian PDEs", Jussieu, February, 2012. pdf

[4] M.Berti, "Quasi-periodic solutions of PDEs", Paris 13 (video conference), February, 2012.

[5] M.Berti, "Quasi-periodic solutions of PDEs ", Institute Advanced studies-Princeton, 12-16 March, 2012 pdf http://www.math.ias.edu/wsd2

[6] M.Berti, "Quasi-periodic solutions of PDEs ", Sissa, April, 2012.

[7] M.Berti, "Quasi-periodic solutions of PDEs. I-II ", Postech, May, 2012, pdf Pohang Mathematics Institute http://math.postech.ac.kr/new/conferences/view/217

[8] M.Berti, "KAM for quasi-linear perturbations of KdV", Capri, June, 2012

[9] M.Berti, "Quasi-periodic solutions of PDEs ", Roma La Sapienza, July, 2012

[10] M.Berti, "Quasi-periodic solutions of PDEs", Ascona, July, 2012 pdf

[11] M.Berti, "KAM theory for derivative wave equations", Roma 3, September, 2012, pdf

[12] M.Berti, "KAM theory for for quasi-linear and fully nonlinear perturbations of KdV", Roma La sapienza, November, 2012,

[13] M.Berti, "KAM for quasi-linear and fully nonlunear perturbations of KdV", Marseille, November 2012 pdf

[14] M.Berti, "KAM for quasi-linear Hamiltonian perturbations of KdV", Zurich, May 2013

[15] M.Berti, "KAM for quasi-linear Hamiltonian perturbations of KdV", Toronto, May 2013

[16] M.Berti, "KAM for quasi-linear Hamiltonian perturbations of KdV", Marseille, June 2013

[17] M.Berti, "KAM for quasi-linear KdV equations", Oberwolfach, July, 2013