The search session has expired. Please query the service again.

Displaying similar documents to “Transversal intersection of separatrices and branching of solutions as obstructions to the existence of an analitic integral in many-dimensional system. I. Basic results: Separatrices of hyperbolic periodic points.”

Diffusion times and stability exponents for nearly integrable analytic systems

Pierre Lochak, Jean-Pierre Marco (2005)

Open Mathematics

Similarity:

For a positive integer n and R>0, we set B R n = x n | x < R . Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian h r = 1 2 r 1 2 + . . . 1 2 r n - 1 2 + r n on 𝕋 n × B R n , with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of 𝕋 n × B R n , and setting ε j : = h - H j C 0 ( V ) the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly...