17 research outputs found
Symmetries of degenerate center singularities of plane vector fields
Let be a closed unit -disk on the plane centered at the origin ,
and be a smooth vector field such that is a unique singular point of
and all other orbits of are simple closed curves wrapping once around
. Thus topologically is a "center" singularity. Let also
be the group of all diffeomorphisms of which preserve
orientation and orbits of . In arXiv:0907.0359 the author described the
homotopy type of under assumption that the -jet of at
is non-degenerate. In this paper degenerate case is considered. Under
additional "non-degeneracy assumptions" on the path components of
with respect to distinct weak topologies are described.Comment: 21 page, 3 figure