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We consider a $pi$-mode solution of the Fermi-Pasta-Ulam $beta$ system. By perturbing it, we study the system as a function of the energy density from a regime where the solution is stable to a regime, where is unstable, first weakly and then strongly chaotic. We introduce, as indicator of stochasticity, the ratio $rho$ (when is defined) between the second and the first moment of a given probability distribution. We will show numerically that the transition between weak and strong chaos can be interpreted as the symmetry breaking of a set of suitable dynamical variables. Moreover, we show that in the region of weak chaos there is numerical evidence that the thermostatistic is governed by the Tsallis distribution.
We study the original $alpha$-Fermi-Pasta-Ulam (FPU) system with $N=16,32$ and $64$ masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave-wave interaction theory, i.e. we assume that, in the weakly nonlinear regime
In systems of N coupled anharmonic oscillators, exact resonant interactions play an important role in the energy exchange between normal modes. In the weakly nonlinear regime, those interactions may facilitate energy equipartition in Fourier space. W
We perform a thorough investigation of the first FPUT recurrence in the $beta$-FPUT chain for both positive and negative $beta$. We show numerically that the rescaled FPUT recurrence time $T_{r}=t_{r}/(N+1)^{3}$ depends, for large $N$, only on the pa
The lifetimes of localized nonlinear modes in both the $beta$-Fermi-Pasta-Ulam-Tsingou ($beta$-FPUT) chain and a cubic $beta$-FPUT lattice are studied as functions of perturbation amplitude, and by extension, the relative strength of the nonlinear in
The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in textit{thermal equilibrium} are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the chain in therm