Rigorous estimates for a computer-assisted KAM theory
- 1 September 1987
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 28 (9) , 2078-2086
- https://doi.org/10.1063/1.527418
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 experimentsKeywords
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