Other
Scientific paper
May 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010dda....41.0903v&link_type=abstract
American Astronomical Society, DDA meeting #41, #9.03; Bulletin of the American Astronomical Society, Vol. 41, p.934
Other
Scientific paper
The low-dimensional model of the dynamics of a galaxy that is described elsewhere at this meeting is applied to a study of chaos in the axisymmetric oscillations of an axisymmetric galaxy. The basic equations of the model are the tensor virial equations reduced to a system of ordinary differential equations governing the semi-axes of a spheroid that characterizes the size and shape of the galaxy. The model thus represents the dynamics of a galaxy as the dynamics of an oscillator in two degrees of freedom. Solutions of the governing equations are examined for manifestations of chaos. The criteria for chaotic behavior that are adopted here are dissolution of invariant curves in Poincare return maps and sensitivity of the motions to small changes in their initial conditions. The regular oscillations of the model are generally quasi-periodic with two frequency components. The periodic oscillations are a "radial” oscillation, in which the semi-axes of the characteristic spheroid oscillate in phase, and a "Kelvin-like” oscillation, in which the semi-axes in the equatorial plane oscillate out of phase with the oscillation of the semi-axis aligned along the axis of symmetry. Manifestations of chaos appear in certain oscillations of sufficiently large amplitudes. For example, the radial oscillation of a spherical galaxy undergoes period doubling and is eventually surrounded by a sea of chaotic oscillations. Other examples of the transition from order to chaos in the model will also be presented.
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