Stability in Steller Dynamics and Bifurcation in Symmetric Hamiltonian Systems
Yieh-Hei Wan Principal Investigator
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8901645 Wan The principal investigator will study the stability of equilibria in stellar dynamics and bifurcation in abstract Hamiltonian systems which possess certain symmetry. For stability problems in collisionless spherical systems, the principal investigator intends to modify the so-called energy-Casimir method in its Hamiltonian setting so as to include inequality constraints. This method has been proven to be successful in stability problems of fluids and plasmas. The immediate goal is to establish the nonlinear stability of certain spherically symmetric equilibria which have been studied previously by Antonov. Motivated by recent results on vortex dynamics the principal investigator also plans to analyze the stability and bifurcation of equilibria and periodic orbits in a symmetric Hamiltonian system (with a reversion). Particular emphasis will be placed on stability computations and on the role played by reversibility of these systems, in the presence of symmetry. Nonlinear stability questions are of fundamental importance in stellar dynamics. The results may be used to explain the appearance of spherical galaxies and globular star clusters. Results on symmetric Hamiltonian systems will be applicable to a wide range of physical systems possessing the same underlying symmetry structure.