CANONICAL REPRESENTATION OF THE DIFFERENTIAL MOTIONS OF AN HAMILTONIAN COSMOS

We present a new analysis of the differential motions of an hamiltonian cosmos with respect to any hamiltonian trajectory taken as reference. We show that the basic differential motions are either of an Anosov hyperbolic type, meaning a stochastic convergence / divergence of neighbouring trajectories, or of an elliptic, oscillating type. Our analysis leads to the construction of a canonical representation of the phase space in finite domains around and along any reference trajectory, which highlights these hyperbolic or elliptic motions.