Chaotic Dynamics of n-Degree of Freedom Hamiltonian Systems

We investigate the connection between local and global dynamics of two N–degree of freedom Hamiltonian systems with different origins describing one–dimensional nonlinear lattices: The Fermi–Pasta–Ulam (FPU) model and a discretized version of the nonlinear Schrödinger equation related to the Bose–Einstein Condensation (BEC). We study solutions starting in the immediate vicinity of simple periodic orbits (SPOs) representing in–phase (IPM) and out–of–phase motion (OPM), which are known in closed form and whose linear stability can be analyzed exactly. Our results verify that as the energy E increases for fixed N , beyond the destabilization threshold of these orbits, all positive Lyapunov exponents Li, i = 1, . . . , N − 1, exhibit a transition between two power laws, Li ∝ E Bk , Bk > 0, k = 1, 2, occurring at the same value of E. The E–mail: [email protected] E–mail: [email protected] ‡ E–mail: [email protected]