Nonautonomous Hamiltonian systems of one degree of freedom close to integrable ones are considered. Let ε be a positive parameter measuring the strength of the perturbation and denote by ε c the critical value at which a given KAM (Kolmogorov–Arnold–Moser) torus breaks down. A computer‐assisted method that allows one to give rigorous lower bounds for ε c is presented. This method has been applied in Celletti–Falcolini–Porzio (to be published in Ann. Inst. H. Poincaré) to the Escande and Doveil pendulum yielding a bound which is within a factor 40.2 of the value indicated by numerical experiments.
Celletti, A., Chierchia, L. (1987). Rigorous estimates for a Computer-assisted KAM theory. JOURNAL OF MATHEMATICAL PHYSICS, 28, 2078 [10.1063/1.527418].
Rigorous estimates for a Computer-assisted KAM theory
CELLETTI, ALESSANDRA;
1987-01-01
Abstract
Nonautonomous Hamiltonian systems of one degree of freedom close to integrable ones are considered. Let ε be a positive parameter measuring the strength of the perturbation and denote by ε c the critical value at which a given KAM (Kolmogorov–Arnold–Moser) torus breaks down. A computer‐assisted method that allows one to give rigorous lower bounds for ε c is presented. This method has been applied in Celletti–Falcolini–Porzio (to be published in Ann. Inst. H. Poincaré) to the Escande and Doveil pendulum yielding a bound which is within a factor 40.2 of the value indicated by numerical experiments.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
