INTEGRABILITY OF NON-KAM HAMILTONIANS
The integrability of Hamiltonians of the type H(P-1,P-2,Q-1,Q-2)= SIGMA(i=1,2) P-i, x G-i(Q-1,Q-2), G-i 2 pi-periodic in Q-1,2, is investigated numerically and analytically. With G-i=omega-i + F-i(Q-1,2) and H-0 = SIGMA(i=1,2) omega-i x P-i, the unperturbed frequencies omega-i=delta H-0/delta P-i are independent of the momenta, and KAM theory cannot be applied. Surface of section plots and Fourier analysis of orbits reveal that most Hamiltonians are integrable. Possibly non-integrable Hamiltonians do not show island plus ergodic region structure but sequences which tend towards infinity. No theory is available to distinguish completely the classes of integrable and non-integrable functions G-i(Q-1,Q-2). In such a theory the problem of small denominators would play an essential role just as in KAM theory.
Bibliographic Reference: ZEITSCHRIFT FUER NATURFORSCHUNG, VOL. 39A (1984), PP. 830-841
Record Number: 1989123018200 / Last updated on: 1987-01-01
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