Symmetries of degenerate center singularities of plane vector fields

Details Symmetries of degenerate center singularities of plane vector fields Symmetries of degenerate center singularities of plane vector fields

2009-07-04

arxiv.org/abs/0907.0737v1

Mathematics

Dynamical Systems

21 page, 3 figures

Scientific paper

Let D be a closed unit 2-disk on the plane centered at the origin O, and F be a smooth vector field such that O is a unique singular point of F and all other orbits of F are simple closed curves wrapping once around O. Thus topologically O is a "center" singularity. Let also Diff(F) be the group of all diffeomorphisms of D which preserve orientation and orbits of F. In arXiv:0907.0359 the author described the homotopy type of Diff(F) under assumption that the 1-jet of F at O is non-degenerate. In this paper degenerate case is considered. Under additional "non-degeneracy assumptions" on F the path components of Diff(F) with respect to distinct weak topologies are described.

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