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

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