We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

}, doi = {10.1016/j.crma.2014.04.012}, url = {http://urania.sissa.it/xmlui/handle/1963/35067}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {2014, title = {KAM for Reversible Derivative Wave Equations}, journal = {Arch. Ration. Mech. Anal.}, volume = {212}, number = {Archive for rational mechanics and analysis;volume 212; issue 3; pages 905-955;}, year = {2014}, pages = {905-955}, publisher = {Springer}, abstract = {We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

}, doi = {10.1007/s00205-014-0726-0}, url = {http://urania.sissa.it/xmlui/handle/1963/34646}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {Berti2013301, title = {KAM theory for the Hamiltonian derivative wave equation}, journal = {Annales Scientifiques de l{\textquoteright}Ecole Normale Superieure}, volume = {46}, number = {2}, year = {2013}, note = {cited By (since 1996)4}, pages = {301-373}, abstract = {We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. {\textcopyright} 2013 Soci{\'e}t{\'e} Math{\'e}matique de France.

}, issn = {00129593}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {2012, title = {The KdV hierarchy: universality and a Painleve transcendent}, journal = {International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099}, number = {arXiv:1101.2602;}, year = {2012}, note = {This article was published in "International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099}, publisher = {Oxford University Press}, abstract = {We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results.}, keywords = {Small-Dispersion limit}, url = {http://hdl.handle.net/1963/6921}, author = {Tom Claeys and Tamara Grava} } @article {2010, title = {A kinetic mechanism inducing oscillations in simple chemical reactions networks}, journal = {Mathematical Biosciences and Engineering 7(2):301-312, 2010}, number = {SISSA;82/2007/M}, year = {2010}, publisher = {American Institute of Mathematical Sciences}, abstract = {It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks.}, doi = {10.3934/mbe.2010.7.301}, url = {http://hdl.handle.net/1963/2393}, author = {Julien Coatleven and Claudio Altafini} } @article {2002, title = {On the K+P problem for a three-level quantum system: optimality implies resonance}, journal = {J.Dynam. Control Systems 8 (2002),no.4, 547}, number = {SISSA;30/2002/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1023/A:1020767419671}, url = {http://hdl.handle.net/1963/1601}, author = {Ugo Boscain and Thomas Chambrion and Jean-Paul Gauthier} } @article {1997, title = {Kam theorem for generic analytic perturbations of the Guler system}, journal = {Z. Angew. Math. Phys. 48 (1997), no. 2, 193-219}, number = {SISSA;136/95/FM}, year = {1997}, publisher = {Springer}, abstract = {We apply here KAM theory to the fast rotations of a rigid body with a fixed point, subject to a purely positional potential. The problem is equivalent to a small perturbation of the Euler system. The difficulty is that the unperturbed system is properly degenerate, namely the unperturbed Hamiltonian depends only on two actions. Following the scheme used by Arnol\\\'d for the N-body problem, we use part of the perturbation to remove the degeneracy: precisely, we construct Birkhoff normal form up to a suitable finite order, thus eliminating the two fast angles; the resulting system is nearly integrable and (generically) no more degenerate, so KAM theorem applies. The resulting description of the motion is that, if the initial kinetic energy is sufficiently large, then for most initial data the angular momentum has nearly constant module, and moves slowly in the space, practically following the level curves of the initial potential averaged on the two fast angles; on the same time the body precesses around the instantaneous direction of the angular momentum, essentially as in the Euler-Poinsot motion. We also provide two simple physical examples, where the procedure does apply.}, doi = {10.1007/PL00001474}, url = {http://hdl.handle.net/1963/1038}, author = {Marta Mazzocco} } @article {1997, title = {Krichever maps, Fa{\`a} di Bruno polynomials, and cohomology in KP theory}, journal = {Lett. Math. Phys. 42 (1997) 349-361}, number = {SISSA;37/97/FM}, year = {1997}, publisher = {Springer}, abstract = {We study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.}, doi = {10.1023/A:1007323118991}, url = {http://hdl.handle.net/1963/3539}, author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa} } @article {1988, title = {A Kellogg property for {\textmu}-capacities}, journal = {Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135}, number = {SISSA;10/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/492}, author = {Gianni Dal Maso and Anneliese Defranceschi} }