Multiplicity of periodic solution with prescribed energy to singular dynamical systems
Le traiettorie paraboliche della meccanica celeste come transizioni di fase minimali
Quanto segue è il testo della conferenza plenaria che ho tenuto al XVIII Congresso dell'Unione Matematica Italiana, in cui ho esposto il contenuto di due lavori in collaborazione con V. Barutello e G. Verzini ([2, 3]). In tali lavori si è sviluppato l'approccio variazionale alle traiettorie paraboliche della Meccanica Celeste, che connettono due configurazioni centrali minimali.
Minimization properties of Hill's orbits and applications to some N-body problems
On the existence of homoclinic solutions for almost periodic second order systems
Density of chaotic dynamics in periodically forced pendulum-type equations
We announce that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics for a dense set of forcing terms in a space of periodic functions with zero mean value. The approach is based on global variational methods.
Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.
Convergence of minimax structures and continuation of critical points for singularly perturbed systems
In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system , as the interspecies scattering length goes to . For this system we consider the associated energy functionals , with -mass constraints, which limit (as ) is strongly irregular. For such functionals, we construct multiple critical points via a common...
Page 1