A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider symplectic/Hamiltonian circle actions on compact symplectic manifolds, which have fixed points. First, we discuss the classification of an action from small numbers of fixed points. Second, we discuss the classification of a Hamiltonian action from low dimensions. Third, we discuss when a symplectic action is Hamiltonian.
