Introduction to the Geometric Theory of Hamiltonian Dynamical Systems
This chapter gives an introduction to the geometric theory of autonomous Hamiltonian systems by studying some local questions about the nature of the solutions in a neighborhood of a point or a periodic solution. The dependences of periodic solutions on parameters is also presented in the case when no drastic changes occur, i.e., when there are no bifurcations. Bifurcations are addressed in Chapter VIII. Several applications to the 3-body problem are given. The chapter ends with a brief introduction to hyperbolic objects and homoclinic phenomena.
KeywordsPeriodic Solution Equilibrium Point Periodic Point Unstable Manifold Stable Manifold
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