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Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom (1982)

Holmes, Philip J. ; Marsden, Jerrold E.

Springer

Communications in mathematical physics 82 (1982), S. 523-544

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01961239

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