On the number of effective integrals in galactic models

Details On the number of effective integrals in galactic models On the number of effective integrals in galactic models

Apr 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35..329m&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 35, April 1985, p. 329-342. SNSF-supported research.

Statistics

Computation

3

Astronomical Models, Computational Astrophysics, Dynamic Models, Elliptical Galaxies, Numerical Integration, Liapunov Functions, Orbits, Oscillators

Scientific paper

Numerical techniques for determining the number of effective integrals in three-degree-of-freedom (3DF) dynamic models of galaxies are compared in sample computations. The computation of the complete set of Liapunov exponents (LCE method) is found to be more useful than the method of triple sections in configuration space or the Stine-Noid (1983) box-counting method in calculations on a triple oscillator with third-order coupling terms, where the possibility of long-term coexistence of one effective integral (aside from the Hamiltonian), corresponding to orbits with simultaneously chaotic and quasi-periodic motion (depending on the coordinates chosen), is demonstrated. In an application of LCE to a 3DF triaxial elliptical-galaxy model, phase-space zones with no nonclassical integral are observed which do not appear in the corresponding 2DF model.

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