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A Lie Algebra of the Symmetries of Liouville’s Equation

Published online by Cambridge University Press:  12 April 2016

Y. Sobouti  and
M.H. Dehghani
Y. Sobouti
Affiliation:
Physics Department and Biruni Observatory, Shiraz University, Shiraz, Iran Center for Theoretical Physics and Mathematics AEO, Tehran, Iran
M.H. Dehghani
Affiliation:
Physics Department and Biruni Observatory, Shiraz University, Shiraz, Iran

Extract

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It is an assumption of traditional stellar dynamics that Liouville’s equation governs the time evolution of stellar systems. An inevitable consequence of such a premise is that (a) at least some modes of instability of stellar systems may be those of Liouville’s equation; and (b) stellar systems might undergo periodic changes of definite patterns in configuration and velocity spaces. For, Liouville’s equation exhibits eigenmodes of oscillation. While it is not feasible to observe the astronomically long periods of oscillations, the patterns of changes, i.e. the eigenfunctions, may be amenable to observation by analyzing the COD records of brightness and velocity distributions on the visible disks of galaxies and globular clusters. This is our motivation for scrutinizing Liouville’s equation, if not for its own merits. The work is a continuation of a series of papers on the symmetries of Liouville’s equation (Sobouti 1989a, b, Sobouti and Samimi 1989).

Type
Part III Stellar Systems and Galaxies
Information
International Astronomical Union Colloquium , Volume 132: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics , 1993 , pp. 233 - 239
Copyright
Copyright © Nova Science Publishers 1993

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