Abstract
In 1985 Franz Rothe [J. Reine Angew Math. 355 (1985) 129–138] found, by means of the thermodynamical equilibrium theory, an asymptotic estimate of the period of solutions of ordinary differential equations originated by predator–prey Volterra–Lotka model. We extend some of the Rothe's ideas to more general systems:
and succeed in calculating the period's asymptotic analytic expression as a function of the energy level. We finally check our result re-obtaining classical period's estimation of some popular Hamiltonian systems. We apply our technique also to a non-linear Hamiltonian system whose period is not available in the literature.
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Foschi, S., Mingari Scarpello, G. & Ritelli, D. Higher Order Approximation of the Period-energy Function for Single Degree of Freedom Hamiltonian Systems. Meccanica 39, 357–368 (2004). https://doi.org/10.1023/B:MECC.0000029367.00112.82
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DOI: https://doi.org/10.1023/B:MECC.0000029367.00112.82