Semi-classical trace formula, isochronous case. Application to conservative systems

Article type: Research Article

Authors: Cassanas, Roch

Affiliations: Mathematisches Institüt Göttingen, Bunsenstr. 3-5, D-37073, Göttingen, Germany. E-mail: [email protected]

Abstract: Under 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.

Journal: Asymptotic Analysis, vol. 55, no. 1-2, pp. 1-32, 2007