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Abstract

THE PROPERTIES OF HAMILTONIANS H{P(1),P(2),Q(1),Q(2)} = P(1)G(1){Q(1),Q(2)} + P(2)G(2){Q(1),Q(2)} WITH ARBITRARY ANALYTIC G(1) AND G(2), 2C-PERIODIC IN Q(1) AND Q(2), ARE INVESTIGATED ANALYTICALLY AND NUMERICALLY. SUCH H CANNOT BE SEPARATED INTO TWO PARTS H = H(0) + H(1), SUCH THAT THE KAM THEOREM WOULD APPLY FOR 3H(1)3<3H(0)3. ORBITS IN PHASE SPACE PROCEED ON NESTED TORI (INTEGRABLE CASES) OR MOVE TOWARDS INFINITY (INTEGRABILITY REMAINS OPEN). NO CHAOTIC REGIONS ARE OBSERVED. FROM THE THEORY OF CIRCLE MAPS IT FOLLOWS THAT NON-KAM HAMILTONIANS ARE INTEGRABLE IF A WINDING NUMBER W IS SUFFICIENTLY IRRATIONAL, A CONDITION WHICH IS ANALOGOUS TO THAT IN THE KAM CASE. IN CONTRAST TO KAM, HOWEVER, THERE IS NO RESTRICTION TO SMALL DEVIATIONS FROM AN UNDISTURBED INTEGRABLE CASE. THE REGIONS OF RATIONAL VS. IRRATIONAL W IN PARAMETER SPACE ARE INTRICATELY INTERSPERSED.

Additional information

Authors: SALAT A MAX-PLANCK-INSTITUT FUER PLASMAPHYSIK, MUENCHEN, D, MAX-PLANCK-INSTITUT FUER PLASMAPHYSIK, MUENCHEN, D
Bibliographic Reference: PHYSICA SCRIPTA, VOL 38, PP 17-21, 1988
Record Number: 1989126214300 / Last updated on: 1989-04-01
Category: PUBLICATION
Available languages: en