Comparison between different methods of estimating of the relaxation times in the FPU model

After a brief review of the Fermi-Pasta-Ulam (FPU) conservative system of N nonlinearly coupled oscillators, this paper addresses two problems: first, comparing two indicators for the equipartition, showing that the results are essentially identical; second, finding a method that allows fast integration to reach the long integration times required in this area. In particular this work proposes a symplectic algorithm based on the Fast Fourier Transform.