MC 6460
Speaker
Giovanni Rastelli | Department of Mathematics, University of Turin, Italy
Title
Twisted products of Hamiltonians: from complete separation to block-separation
Abstract
Classical Staeckel systems, related to complete separation of Hamilton -Jacobi equation, can be understood as the decomposition of a n-dimensional natural Hamiltonian H into n one-dimensional Hamiltonians, given by the separated equations. The n-dimensional dynamics can be reconstructed from the one-dimensional ones up to time-reparametrizations. The characterization of the complete separation is coordinate-free and determined by n quadratic in the momenta first-integrals in involution. The existence of less than n quadratic first-integrals in involution can determine a partial separation (block-separation) of the system, with similar relations between the global and the separated dynamics. All these types of separation arise from a particular twisted-product structure of H. We review the classical results about complete separation and introduce new results and characterization of block-separation.