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