Lower and Upper Bounds for the Splitting of Separatrices of the Pendulum under a Fast Quasiperiodic Forcing Amadeu Delshams Vassili Gelfreich Angel Jorba and Tere M Seara

Lower and Upper Bounds for the Splitting of Separatrices of the Pendulum under a Fast Quasiperiodic Forcing

Quasiperiodic perturbations with two frequencies (1/ε, γ/ε) of a pendulum are considered, where γ is the golden mean number. We study the splitting of the three-dimensional invariant manifolds associated to a twodimensional invariant torus in a neighbourhood of the saddle point of the pendulum. Provided that some of the Fourier coefficients of the perturbation (the ones associated to Fibonacci ...

Exponentially small splitting of separatrices under fast quasiperiodic forcing

We consider fast quasiperiodic perturbations with two frequencies of a pendulum where is the golden mean number The complete system has a two dimensional invariant torus in a neighbourhood of the saddle point We study the splitting of the three dimensional invariant manifolds associated to this torus Provided that the perturbation amplitude is small enough with respect to and some of its Fourie...

Splitting of Separatrices in Hamiltonian Systems and Symplectic Maps Amadeu Delshams Rafael Ram Rez Ros and Tere M Seara

Splitting of Separatrices in Hamiltonian Systems and Symplectic Maps Amadeu Delshams, Rafael Ram Rez-ros and Tere

Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom

The splitting of separatrices for Hamiltonians with 1 2 degrees of freedom h(x; t=") = h0(x) + "ph1(x; t=") is measured. We assume that h(x) = h0(x1; x2) = x 2 2 =2 + V (x1) has a separatrix x(t), h(x; ) is 2 -periodic in , and " > 0 are independent small parameters, and p 0. Under suitable conditions of meromorphicity for x 2 (u) and the perturbation h(x(u); ), the order ` of the perturbation ...