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Recently, based on the classification of the second and third order homogeneous Hamitionan operators Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonia...
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
In recent years there has been a growing interest towards the integrability of systems which, though not Hamiltonian, retain some link to—or common origin with—Hamiltonian systems. One such field is t...
The study of Hamiltonian dynamical systems plays a fundamental role in many different contexts, both in pure and applied mathematics. Indeed, most of the physical laws ruling our everyday lives --the ...
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
We consider a process on T2, which consists of fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the graph n...
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes of representat...
We consider a process on T 2, which consists of the fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the grap...
The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it.Ehrenfest (The Conceptual Foundations of th...
In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following resul...
It is well know that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is wellapproximated by the associated averaged system, ca...
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The ...
We consider here the problem of a "giant spin", with spin quantum number S≫1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model desc...

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