Introduction to the Geometric Theory of Hamiltonian Dynamical Systems

  • Kenneth R. Meyer
  • Glen R. Hall
Part of the Applied Mathematical Sciences book series (AMS, volume 90)


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.


Periodic Solution Equilibrium Point Periodic Point Unstable Manifold Stable Manifold 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Kenneth R. Meyer
    • 1
  • Glen R. Hall
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Mathematics DepartmentBoston UniversityBostonUSA

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