Counting periodic trajectories via topological classical mechanics
For systems with compact phase space and isolated periodic orbits the author counts the number of periodic trajectories by applying a path- integral approach to classical Hamiltonian mechanics developed in the author's previous papers [Phys. Lett. B 201, 525-528 (1988), Phys. Rev. D 40, 3363-3377 (1989) (together with \textit{M. Reuter} and \textit{W. D. Thacker}), and Phys. Rev. D 46, 757-765 (1992) (together with \textit{M. Reuter} and \textit{W. D. Thacker})]. Namely, it is shown that the number of periodic trajectories (of the same period) in phase space is equal to the Euler number of the underlying phase space.
scientific article; zbMATH DE number 621857