# On GIT quotients of the symplectic group, stability and bifurcations of symmetric orbits

@inproceedings{Frauenfelder2021OnGQ, title={On GIT quotients of the symplectic group, stability and bifurcations of symmetric orbits}, author={Urs Frauenfelder and Agust{\'i}n Moreno}, year={2021} }

We provide topological obstructions to the existence of orbit cylinders of symmetric orbits, for mechanical systems preserved by antisymplectic involutions (e.g. the restricted three-body problem). Such cylinders induce continuous paths which do not cross the bifurcation locus of suitable GIT quotients of the symplectic group, which are branched manifolds whose topology provide the desired obstructions. Namely, the complement of the corresponding loci consist of several connected components… Expand

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