We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. 2000AMS subject classification: 37K55, 35L05.

We study the regularity and well-posedness of local, first-order forward-backward mean field games system, assuming a polynomially growing cost function Hamiltonian quadratic growth. consider systems terminal data that are strictly monotone in density two different regimes depending on whether there exists lower bound for running function. The work relies transformation due to P.-L. Lions, whic...

We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants critical Lane-Emden system and analogous Brezis-Nirenberg problem. find a function governs points rates, observing that it reflects strong nonlinear characteristic system. By using it, we also prove single solution exists general domains, examples contractible w...

We consider infinite dimensional Hamiltonian systems. First we prove the existence of “Cantor manifolds” of elliptic tori -of any finite higher dimensionaccumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are “branching” points of other Cantor manifolds of higher dimensional tori. We also provide a ...

We study the existence of classical solutions to a broad class local, first order, forward-backward extended mean field games systems, that includes standard games, with congestion, and type control problems. work strictly monotone cost may be fully coupled Hamiltonian, which is assumed have superlinear growth. Following previous on order system, we prove smooth under coercivity condition ensur...

This talk deals with a remarkable integrable discretization of the SO(3) Euler top introduced in [1] by R. Hirota and K. Kimura. A class of implicit discretizations of the Euler top sharing the integrals of motion with the continuous system has been presented and studied in [2]. The Hirota-Kimura discretization of the Euler top leads to an explicit map. Its integrability is proven by finding tw...

In this paper, we consider analytic perturbations of an integrable Hamiltonian system in a given resonant surface. It is proved that, for most frequencies on the resonant surface, the resonant torus foliated by nonresonant lower dimensional tori is not destroyed completely and that there are some lower dimensional tori which survive the perturbation if the Hamiltonian satisfies a certain nondeg...

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions...