| Abstract: |
| This talk deals with the stability analysis for equilibria of Euler equations on real semi-simple Lie algebras. Around 1980, Mishchenko and Fomenko have introduced a class of generalized Euler equations on arbitrary semi-simple Lie algebras and proved their complete integrability. Precisely speaking, for an arbitrary Cartan subalgebra in the real semi-simple Lie algebra, there is associated a family of Euler equations. Mishchenko and Fomenko have proved that the restriction of such Euler equations to a generic adjoint orbit is completely integrable in the sense of Liouville. Rather recently, the stability of equilibria has been analyzed for Mishchenko-Fomenko rigid body dynamics on real semi-simple Lie algebras of type A, on compact real Lie algebras, and on split real form of complex semi-simple Lie algebras. In this talk, the stability analysis is performed for isolated equilibria on a generic adjoint orbit for Euler equation on any real semi-simple Lie algebra associated with an arbitrary Cartan subalgebra. The stability property of the equilibria is characterized by the types of the roots corresponding to the complexification of the Cartan subalgebra. |
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