Bernoulli sequences and trajectories in the anisotropic Kepler problem

摘要: The anisotropic Kepler problem is investigated in order to establish the one‐to‐one relation between its trajectories and binary Bernoulli sequences. Hamiltonian has a quadratic kinetic energy with an mass tensor spherically symmetric Coulomb energy. Only two dimensions negative (bound states) are discussed. previous study of this system was based on extensive numerical computations, but present work uses only analytical arguments. After review earlier results, their relevance understanding classical quantum mechanics emphasized. main new result show existence at least one trajectory corresponding each sequence. proof employs number unusual mathematical tools, although they all elementary. In particular, virial as function momenta (rather than action position coordinates) plays crucial role. Also, different ...