Partial separability and symplectic-Haantjes manifolds

• DOI: 10.1007/s10231-024-01462-y
• Publication Date: 2024-07-02T12:02:20Z
• Authors: Daniel Reyes; Piergiulio Tempesta; Giorgio Tondo
• Keywords: 37J35, 53A45, 70H20; Mathematics - Symplectic Geometry; FOS: Mathematics; Symplectic Geometry (math.SG); FOS: Physical sciences; Mathematical Physics (math-ph); 0101 mathematics; 01 natural sciences; Mathematical Physics

Abstract A theory of partial separability for classical Hamiltonian systems is proposed in the context Haantjes geometry. As a general result, we show that knowledge non-semisimple symplectic-Haantjes manifold given system sufficient to construct sets coordinates (called Darboux-Haantjes coordinates) allow both associated Hamilton-Jacobi equations and block-diagonalization operators corresponding algebra. We also introduce novel class systems, characterized by existence generalized Stäckel matrix, which construction are partially separable. They widely generalize known families separable systems. The new can be described terms semisimple but non-maximal-rank manifolds.