Persistence of Hamiltonian relative periodic orbits. (Q1414654)

Relative periodic orbits typically appear as trajectories of an equivariant dynamical system which are periodic in a co-moving or co-rotating coordinate system. Here, a result on the persistence of relative periodic orbits in Hamiltonian systems with a noncompact nonfree group action is proved. To this end, the author studies the algebraic variety of drift-momentum pairs. Her main theorem states that a relative periodic orbit which is nondegenerate and has regular drift-momentum pair modulo isotropy persists, i.e., it is contained in a family of relative periodic orbits with the same spatio-temporal symmetry. In addition, the author proves a result on symmetry breaking persistence where the bifurcating branch has a smaller spatio-temporal symmetry. The results are applied to the dynamics of a deformable body in an irrotational fluid.