Hamiltonian Systems

  • Jan A. Sanders
  • Ferdinand Verhulst
Part of the Applied Mathematical Sciences book series (AMS, volume 59)


In Hamiltonian mechanics, the small parameter necessary to do asymptotics is usually obtained by localizing the system around some wellknown solution, e.g. an equilibrium. As we shall see, the part played by the small parameter in the normal form of the Hamiltonian determines the asymptotic estimates which we can obtain. In the various resonance cases which we shall discuss, these estimates take different forms the theory of which is based on the preceding chapters with special extensions for the Hamiltonian context.


Periodic Orbit Normal Form Normal Mode Hamiltonian System Discrete Symmetry 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Jan A. Sanders
    • 1
  • Ferdinand Verhulst
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.Mathematical InstituteState University of UtrechtUtrechtThe Netherlands

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