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    Boulanger2019_Article_Higher-derivativeHarmonicOscil.pdf (477.0Ko)
    Date
    2019-01-06
    Auteur
    Boulanger, Nicolas
    BUISSERET, Fabien
    DIERICK, Frédéric
    White, Olivier
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    Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants

    Résumé
    he status of classical stability in higher-deriv- ative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this prop- erty are Nekhoroshev’s estimates relying on the action-angle formulation of classical mechanics. The latter formulation can be reached provided the Hamiltonian is separable, which is the case for higher-derivative harmonic oscillators. The Pais–Uhlenbeck oscillators appear to be the only type of higher-derivative harmonic oscillator with stable classical dynamics. A wide class of interaction potentials can even be added that preserve classical stability. Adiabatic invariants are built in the case of a Pais–Uhlenbeck oscillator slowly changing in time; it is shown indeed that the dynamical sta- bility is not jeopardised by the time-dependent perturbation

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