2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118048In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graff and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on sub-manifolds.LaTeX, 17 pagesDynamical SystemsMathematical Physics37J40; 70H05; 70K60text