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Collision orbits in the anisotropic Kepler problem. (English) Zbl 0382.58015


MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37C75 Stability theory for smooth dynamical systems
37D99 Dynamical systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems
37N99 Applications of dynamical systems
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References:

[1] Alekseev, V.M.: Quasirandom dynamical systems I, II, III. Math. USSR-Sb.6, 489-498 (1969) · Zbl 0198.56903
[2] Conley, C., Easton, R.: Isolated invariant sets and isolating blocks. Trans. Amer. Math. Soc.158, 35-61 (1971) · Zbl 0223.58011 · doi:10.1090/S0002-9947-1971-0279830-1
[3] Conley, C.: Some applications of topology in differential equations. Preprint, University of Wisconsin, Madison, Wisconsin · Zbl 0339.34047
[4] Devaney, R.: Homoclinic orbits in Hamiltonian systems. J. Differential Equations21, 431-438 (1976) · Zbl 0343.58005 · doi:10.1016/0022-0396(76)90130-3
[5] Easton, R.: Isolating blocks and symbolic dynamics. J. Differential Equation17, 96-118 (1975) · Zbl 0293.58011 · doi:10.1016/0022-0396(75)90037-6
[6] Gutzwiller, M.C.: J. Mathematical Phys.8, 1979 (1967);10, 1004 (1969);11, 1971 (1970); and12, 343 (1971) · doi:10.1063/1.1705112
[7] Gutzwiller, M.C.: The anisotropic Kepler problem in two dimensions. J. Mathematical Phys.14, 139-152 (1973) · doi:10.1063/1.1666164
[8] Gutzwiller, M.C.: Bernoulli sequences and trajectories in the anisotropic Kepler problem. (To appear) · Zbl 0684.70021
[9] Hirsch, M., Pugh, C., Shub, M.: Invariant manifolds. (To appear)
[10] McGehee, R.: Triple collision in the collinear three-body problem. Inventiones math.27, 191-227 (1974) · Zbl 0297.70011 · doi:10.1007/BF01390175
[11] McGehee, R.: Double collisions for non-Newtonian potentials. (To appear) · Zbl 0498.70015
[12] Moser, J.: Stable and random motions in dynamical systems. Princeton, N.J.: University Press 1973 · Zbl 0271.70009
[13] Pollard, H.: Mathematical Introduction to Celestial Mechanics. Prentice Hall: Englewood Cliffs, N.J. 1966 · Zbl 0141.23803
[14] Sacker, R.: A perturbation theorem for invariant manifolds and Hölder continuity. J. Math. Mech.18, 705-762 (1969) · Zbl 0218.34046
[15] Silnikov, L.P.: Soviet Math. Dokl.8, 54-58 (1967)
[16] Smale, S.: Differentiable dynamical systems. Bull. Amer. Math. Soc.73, 747-817 (1967) · Zbl 0202.55202 · doi:10.1090/S0002-9904-1967-11798-1
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