A recently proposed algorithm for the estimate of the threshold above which a certain torus disappears, which combines classical Birkhoff normalization procedure with KAM theory, is reconsidered and improved. This is done by studying the particular case of the forced pendulum Hamiltonian {Mathematical expression}, and considering the golden torus. We find that there exists an optimal order N of normalization, and the ratio between the estimate thus obtained and the experimental value turns out to be ∼19. A possible explanation of such result is also suggested.
On the numerical optimization of KAM estimates by classical perturbation theory / A. Celletti, A. Giorgilli. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - 39:5(1988 Sep), pp. 743-747. [10.1007/BF00948734]
On the numerical optimization of KAM estimates by classical perturbation theory
A. GiorgilliUltimo
1988
Abstract
A recently proposed algorithm for the estimate of the threshold above which a certain torus disappears, which combines classical Birkhoff normalization procedure with KAM theory, is reconsidered and improved. This is done by studying the particular case of the forced pendulum Hamiltonian {Mathematical expression}, and considering the golden torus. We find that there exists an optimal order N of normalization, and the ratio between the estimate thus obtained and the experimental value turns out to be ∼19. A possible explanation of such result is also suggested.
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