2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125477Under conditions of clean flow we compute the leading term in the STF when the set of periods of the energy surface is discrete. Comparing to the case of non-degenerate periodic orbits, we obtain a supplementary term which is given in terms of the linearized flow. As particular cases, we give a STF for quadratic Hamiltonians and we obtain the Berry-Tabor formula for integrable systems. For conservative systems (i.e. systems with several first integrals), we give practical conditions to get a clean flow and interpret the leading term of the STF for a compact symmetry. We give several examples to illustrate our computation.24 pagesMathematical PhysicsSpectral TheoryPrimary 81Q20, Secondary 81R12, Tertiary 81R30text