INTEGRABILITY OF NON-KAM HAMILTONIANS
Integrability of Hamiltonians of the type H(P-1,P-2,!-1,Q-2) + z < SIGMA-i + z < 1,2- P-i G-i(Q-1,Q-2), G-i 2pi-periodic in Q-1, Q-2, is investigated numerically and analytically. With G-i + z < omega-i +< F-i(Q-1,Q-2) and H-O + z < i -+ z < SIGMA-1,2 omega-iP-i, the unperturbed frequencies omega-i + z < p-deltaH-o/p-deltaP-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: WRITE TO MAX-PLANCK-INSTITUT FUER PLASMAPHYSIK,8046 GARCHING BEI MUENCHEN (GERMANY) MENTIONING REPORT 6/238, 1984
Record Number: 1989123043700 / Last updated on: 1987-01-01
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