A generalization of Hopf's bifurcation problem

Mathematics

Scientific paper

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Branching (Mathematics), Dissipation, Transformations (Mathematics), Celestial Mechanics, Liapunov Functions

Scientific paper

Hopf's bifurcation problem is generalized, beginning with a study of the behavior of a 2-dimensional, 2 pi-periodic system. The method of averaging (second order procedure, thus constructing a 2 pi-periodic diffeomorphism) is used in this dissipative system. Also applied is the theorem of the existence of invariant tori for dissipative systems, which guarantees a stable and attractive manifold.

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