86 citations · 197 across the 14 of their papers we have counts for
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Tonelli Hamiltonians without conjugate points and integrability
Marc Arcostanzo, Marie-Claude Arnaud, Philippe Bolle +1
We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $T^*\T^n$ of the -dimensional torus that have no conjugate points are integrable, i.e. $T^*\T^n$…
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…
Diffusion time and splitting of separatrices for 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…