The anisotropic Kepler problem in two dimensions

摘要: The classical trajectories are investigated for a particle with an anisotropic mass tensor in ordinary Coulomb potential. For negative energies (bound states) these isomorphic the geodesics on Riemannian surface which can be immersed Euclidean space and looks like ``double snail.'' vanishing energy (or near collision) equations of motion reduced to autonomous system whose fully discussed. On basis extensive numerical computations, it has been possible give simple, yet complete description all energy. A binary sequence is associated any trajectory where each term gives sign position coordinate consecutive intersections ``heavy'' axis. If represented by two real numbers, one‐to‐one continuous map from them initial conditions constructed. Thus, Poincare equivalent shift Bernoulli scheme (tossing coin), periodic orbits obtained systematically. number discussed illustrate consequences isomorphism sequences. Finally, baker transformation its use finding connect given endpoints, mentioned.