A normally elliptic Hamiltonian bifurcation

  • H. W. Broer
  • S. N. Chow
  • Y. Kim
  • G. Vegter
Original Papers


A universal local bifurcation analysis is presented of an autonomous Hamiltonian system around a certain equilibrium point. This central equilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Main emphasis is given to the 2 degrees of freedom case where these other eigenvalues are purely imaginary. By normal form techniques and Singularity Theory unfoldings are obtained, having ‘integrable’ approximations related to the Elliptic and Hyperbolic Umbilic Catastrophes


Normal Form Equilibrium Point Hamiltonian System General Position Singularity Theory 
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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • H. W. Broer
    • 1
  • S. N. Chow
    • 2
  • Y. Kim
    • 3
  • G. Vegter
    • 4
  1. 1.Department of MathematicsUniversity of GroningenAV GroningenThe Netherlands
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of MathematicsUniversity of UlsanUlsanSouth Korea
  4. 4.Department of Computing ScienceUniversity of GroningenAV GroningenThe Netherlands

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