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

1 aBaldi, P1 aBerti, Massimiliano1 aMontalto, Riccardo uhttp://urania.sissa.it/xmlui/handle/1963/3506700608nas a2200157 4500008004100000245004900041210004900090260001300139300001200152490000800164520016500172100002400337700001700361700002100378856005100399 2014 en d00aKAM for Reversible Derivative Wave Equations0 aKAM for Reversible Derivative Wave Equations bSpringer a905-9550 v2123 aWe prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3464600759nas a2200157 4500008004100000022001300041245006000054210006000114300001200174490000700186520025600193100002400449700001700473700002100490856009000511 2013 eng d a0012959300aKAM theory for the Hamiltonian derivative wave equation0 aKAM theory for the Hamiltonian derivative wave equation a301-3730 v463 aWe 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. © 2013 Société Mathématique de France.

1 aBerti, Massimiliano1 aBiasco, Luca1 aProcesi, Michela uhttps://www.math.sissa.it/publication/kam-theory-hamiltonian-derivative-wave-equation01113nas a2200133 4500008004100000245006400041210005900105260002800164520069000192653002700882100001600909700001800925856003600943 2012 en d00aThe KdV hierarchy: universality and a Painleve transcendent0 aKdV hierarchy universality and a Painleve transcendent bOxford University Press3 aWe 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.10aSmall-Dispersion limit1 aClaeys, Tom1 aGrava, Tamara uhttp://hdl.handle.net/1963/692100781nas a2200121 4500008004300000245008400043210006900127260004800196520033500244100002200579700002200601856003600623 2010 en_Ud 00aA kinetic mechanism inducing oscillations in simple chemical reactions networks0 akinetic mechanism inducing oscillations in simple chemical react bAmerican Institute of Mathematical Sciences3 aIt 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.1 aCoatleven, Julien1 aAltafini, Claudio uhttp://hdl.handle.net/1963/239300435nas a2200121 4500008004100000245008600041210006900127260001800196100001700214700002200231700002400253856003600277 2002 en d00aOn the K+P problem for a three-level quantum system: optimality implies resonance0 aKP problem for a threelevel quantum system optimality implies re bSISSA Library1 aBoscain, Ugo1 aChambrion, Thomas1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/160101558nas a2200109 4500008004100000245007100041210006900112260001300181520119800194100002001392856003601412 1997 en d00aKam theorem for generic analytic perturbations of the Guler system0 aKam theorem for generic analytic perturbations of the Guler syst bSpringer3 aWe 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.1 aMazzocco, Marta uhttp://hdl.handle.net/1963/103801059nas a2200133 4500008004300000245007500043210007000118260001300188520062700201100002100828700001800849700002200867856003600889 1997 en_Ud 00aKrichever maps, Faà di Bruno polynomials, and cohomology in KP theory0 aKrichever maps Faà di Bruno polynomials and cohomology in KP the bSpringer3 aWe 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.1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/353900332nas a2200109 4500008004100000245004100041210003800082260001800120100002100138700002800159856003500187 1988 en d00aA Kellogg property for µ-capacities0 aKellogg property for µcapacities bSISSA Library1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/492