Applied Math Seminar I Giovanni Rastelli, Twisted products of Hamiltonians: from complete separation to block-separation

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.