The effect of weak dissipation on the system with Arnold’s diffusion

Saratov State University , Russia

We investigate the effect of weak dissipation on the hamiltonian system with more than two degrees of freedom. It is well known that in such systems the resonance stochastic layers cross each other forming some web in the phase space. This makes the unlimited diffusion possible for any small values of non-integrable perturbation unlike the systems with 2 degrees of freedom. This diffusion was revealed by V.I. Arnold and is known as Arnold’s diffusion. We consider the system of two coupled twist maps [1] and study the transformations of the actions plane structure by calculating both the orbits of the map with dissipative perturbations and its Lyapunov exponents. It was found that at low values of dissipation in the system attractors appear that are fixed points and invariant curves. Although attractors are regular the chaotic transition process is observed and its duration depends on the initial position so that the regions with the slowest transition form the square-like lattice. References [1] M. Guzzo, E. Lega, C. Froeschle //Noninearity, 2006, v.19, p.1049