Reference systems for splitting of separatrices

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 ...

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

Exponentially small splitting of separatrices for perturbed integrable standard like maps

The splitting of separatrices for the standard-like maps is measured. For even entire perturbative potentials V (y) = P n2 V n y 2n such that b V (2) 6 = 0, where b V () = P n2 V n 2n?1 =(2n ? 1)! is the Borel transform of V (y), the following asymptotic formula for the area A of the lobes between the perturbed separatrices is established A = 8 b V (2)" e ? 2 =h h 1 + O(h 2) i (" = o(h 6 ln ?1 ...

Splitting of Separatrices for (fast) Quasiperiodic Forcing

At the end of the last century, H. Poincar e 7] discovered the phenomenon of sepa-ratrices splitting, which now seems to be the main cause of the stochastic behavior in Hamiltonian systems. He formulated a general problem of Dynamics as a perturbation of an integrable Hamiltonian system