Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
Copyright policy )Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
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.
- Cornell University United States
- University of California, Berkeley United States
- California Institute of Technology United States
Hamilton's equations, 58F30, 70K50, 70H99, system consisting of the simple pendulum and the harmonic oscillator, Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits, 530, 58F15, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, 510, Dynamical systems with hyperbolic behavior, introducing horseshoes into the dynamics, Melnikov theory
Hamilton's equations, 58F30, 70K50, 70H99, system consisting of the simple pendulum and the harmonic oscillator, Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits, 530, 58F15, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, 510, Dynamical systems with hyperbolic behavior, introducing horseshoes into the dynamics, Melnikov theory
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