REDUCTION THEORY, ELLIPTIC SOLITONS AND INTEGRABLE SYSTEMS

EMMA PREVIATO

Abstract. One goal of this paper is to connect two of the thesis topics of Sophie Kowalevski, namely reduction theory for abelian functions and integrability of a dynamical system. Part I is a digest of classical and current research on splittable Jacobians and curves with automorphisms. Part II is a collection of applications of the splittable situation to the explicit integration of Hamiltonian systems of finite and infinite dimension. Both fields are full of open questions, and the last section in each part is a collection of such.