Communications in Mathematical Physics

, Volume 82, Issue 4, pp 523–544 | Cite as

Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom

  • Philip J. Holmes
  • Jerrold E. Marsden


This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns perturbations of the uncoupled system consisting of the simple pendulum and the harmonic oscillator. We show that small coupling perturbations with, possibly, the addition of positive and negative damping breaks the integrability by introducing horseshoes into the dynamics.


Neural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Philip J. Holmes
    • 1
  • Jerrold E. Marsden
    • 2
  1. 1.Department of Theoretical and Applied MechanicsCornell UniversityIthacaUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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