For large system size, the rescaled beta-FPUT recurrence time is a function only of S = E beta (N+1), linear for small |S| and scaling as |S|^{-1/2} for large |S|, in both positive and negative beta chains.
(C25) We note that in equations (C9-C25), all of the nonlinear frequencies are calculated to first order in β
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The $\beta$ Fermi-Pasta-Ulam-Tsingou Recurrence Problem
For large system size, the rescaled beta-FPUT recurrence time is a function only of S = E beta (N+1), linear for small |S| and scaling as |S|^{-1/2} for large |S|, in both positive and negative beta chains.