Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems

Abstract

In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find the solutions of the equations of motion by quadratures.

arXiv commentComments are welcome. arXiv admin note: text overlap with arXiv:2211.02970

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