Bifurcation diagram of the system of bending of 3D regular pentagons
- Damien Bouloc
This is the bifurcation diagram, i.e. the image of the momentum map, of the integrable Hamiltonian system of bending of 3D polygons introduced by Kapovich and Millson, in the case n=5 and r=(1,1,1,1,1).
- In the interior of the diagram, the (regular) fibers are tori of dimension 2. - On the edges of the diagram, the (singular) fibers are tori of dimension 1. - At the vertices G, H and I, the (singular) fibers are reduced to a point. - At the vertices F and J, the fibers are spheres of dimension 2. Note that despite being singular fibers, they have maximal dimension.