Chaos in low-dimensional hamiltonian maps

Symplectic maps with more than two degrees of freedom constructed by coupling N area-preserving Chiricov-Taylor standard maps are investigated by numerical methods. We find the asymptotic (for N→∞) distribution of the N positive Lyapunov exponents which is attained already for surprisingly small N. To test the errors in calculating Lyapunov exponents from finite parts of trajectories we calculate the fluctuations of the effective Lyapunov exponents as a function of the number of iterations and find a nontrivial decay on time scales decreasing with increasing degree of freedom. These fluctuations are due to clinging of trajectories to regular orbits.