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We consider a $\pi$-mode solution of the Fermi-Pasta-Ulam $\beta$ system. Byperturbing it, we study the system as a function of the energy density from aregime where the solution is stable to a regime, where is unstable, firstweakly and then strongly chaotic. We introduce, as indicator of stochasticity,the ratio $\rho$ (when is defined) between the second and the first moment of agiven probability distribution. We will show numerically that the transitionbetween weak and strong chaos can be interpreted as the symmetry breaking of aset of suitable dynamical variables. Moreover, we show that in the region ofweak chaos there is numerical evidence that the thermostatistic is governed bythe Tsallis distribution.

Thermostatistics in the neighborhood of the $\pi$-mode solution for the Fermi-Pasta-Ulam $\beta$ system: from weak to strong chaos