Qualitative Analysis of the Anistropic Kepler Problem.

Intro -- TABLE OF CONTENTS -- 0: INTRODUCTION -- I: THE KEPLER PROBLEM -- (I.1) Formulation -- (I.2) Collision manifold -- (I.3) Infinity manifolds -- (I.4) Summary on the singularities -- (I.5) Heteroclinic orbits -- (I.6) Global flow -- (I.7) Poincaré map -- II: THE ANISOTROPIC KEPLER PROBLEM -- (II.1) Formulation -- (II.2) Symmetries -- (II.3) The Collision manifold -- (II.4) The Infinity manifolds -- (II.5) Invariant manifolds I[sub(h)] -- (II.6) Heteroclinic orbits -- (II.7) The flow on the collision manifold -- III: THE FLOW FOR NON-NEGATIVE ENERGY LEVELS -- (III.1) The case h=0 -- (III.2) The case h&gt -- 0 -- IV: THE FLOW ON NEGATIVE ENERGY LEVELS WHEN μ&gt -- 9/8 -- (IV.1) The intersection of the invariant manifolds with the surface of section v=0 -- (IV.2) The Poincaré maps g,f and h on v=0 -- (IV.3) The invariant manifolds under g and f -- (IV.4) Geometrical interpretation of the neighbourhoods of the invariant manifolds -- (IV.5) Regions with a constant number of crossings with the q[sub(2)]…axis, the map S[sub((θ[sub(0)],μ))] -- (IV.6) Basic sets for dynamical description -- (IV.7) A subshift as subsystem of h -- (IV.8) Gutzwiller's Theorem -- V: THE FLOW ON NEGATIVE ENERGY LEVELS WHEN 1&lt -- μ≤ 9/8 -- (V.l) The intersection of the invariant manifolds with the surface of section v=0 -- (V.2) Dynamical description -- VI: SYMMETRIC PERIODIC ORBITS -- (VI.1) Definitions and preliminary results -- (VI.2) The case μ=1 -- (VI.3) The case μ&gt -- 9/8 -- APPENDIX -- REFERENCES.

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