Construction of invariant tori in chaotic regions

Details Construction of invariant tori in chaotic regions Construction of invariant tori in chaotic regions

Jul 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phrve..52.1193k&link_type=abstract

Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 52, Issue 1, July 1995, p

Nonlinear Sciences

Chaotic Dynamics

7

Chaotic Dynamics, Stellar Dynamics And Kinematics

Scientific paper

Following the introduction of a general method for constructing approximate invariant tori of a given Hamiltonian H [M. Kaasalainen and J. J. Binney, Phys. Rev. Lett. 73, 2377 (1994)], it is shown that the scheme can be applied to Hamiltonians with globally chaotic regions as well. The created tori are proper in that (i) they are geometrically credible and fill chaotic regions in an orderly way; (ii) their frequencies are consistent with those of the closed orbits of H; and (iii) for short time periods, motion on them approximates motion in H. One of the examples is given in a rotating frame of reference, with a Hamiltonian more complicated than the usual sum of kinetic and potential energies.

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