On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems

In this text we take up the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. We first conduct a geometric study, which for a large part is not restricted to the perturbative situation of near integrable systems.[...] The next technical input is the introduction of a canonically invariant scheme for the computation of the splitting matrix.