We investigate with numerical methods the celebrated Fermi-Pasta-
Ulam model, a chain of non-linearly coupled oscillators with identical masses. We
are interested in the evolution towards equipartition when energy is initially given
to one or a few modes. In previous works we considered the initial energy being
given on the lower part of the spectrum. Using the spectral entropy as a numerical
indicator we obtained a strong indication that the relaxation time to equipartition
increases exponentially with an inverse power of the specific energy. Such a scaling
appears to remain valid in the thermodynamic limit. In this paper we explore the
dynamics obtained with the initial excitation on the high frequency modes, and we
obtain also in this case indication of exponentially long times to equipartition.
Mathematics Subject Classification:
Primary: 34C15, 70K55; Secondary: 34C2.
Simone Paleari, Tiziano Penati. Equipartition times in a Fermi-Pasta-Ulam system. Conference Publications,
Meilan Cai, Maoan Han.
Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters.
Communications on Pure & Applied Analysis,