Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
Given a complex analytical Hamiltonian system, we prove that a necessary condition for its meromorphic complete integrability is the commutativity of the identity component of the Galois group of each variational equation of arbitrary order along any integral curve. This was conjectured by the first author based on a suggestion …