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A Birkhoff--Lewis Type Theorem for Some Hamiltonian Pdes
Dario Bambusi, Massimiliano Berti
In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accum…
Periodic orbits close to elliptic tori and applications to the three-body problem
Massimiliano Berti, Luca Biasco, Enrico Valdinoci
We prove, under suitable non-resonance and non-degeneracy ``twist'' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with large…
Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
Massimiliano Berti, Luca Biasco, Philippe Bolle
We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) -perturbation which does not preserve the unperturbed…
Fast Arnold Diffusion in three time scale systems
Massimiliano Berti, Philippe Bolle
We consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based…
Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems
Massimiliano Berti, Philippe Bolle
We consider the problem of Arnold's diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusi…
Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium
Massimiliano Berti, Philippe Bolle
We consider autonomous Lagrangian systems with two degrees of freedom, having an hyperbolic equilibrium of saddle-saddle type (that is the eingenvalues of the linearized system abo…