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Instability of the Periodic Motion of a Particle Interacting with a Scalar Wave Field

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Abstract:

We consider the system of a point particle, accelerated through a confining potential, and interacting with a scalar wave field. We prove that the periodic solutions of the linearized system (which has an eigenvalue embedded in the continuous spectrum) do not survive perturbation through the nonlinearity, if some “mode” of the wave field does not couple to the particle.

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Received: 18 August 1997 / Accepted: 9 December 1997

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Kunze, M. Instability of the Periodic Motion of a Particle Interacting with a Scalar Wave Field . Commun. Math. Phys. 195, 509–523 (1998). https://doi.org/10.1007/s002200050400

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  • DOI: https://doi.org/10.1007/s002200050400

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