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Delay Equations and Radiation Damping

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arxiv gr-qc/0101122 v3 pith:67JGA365 submitted 2001-01-30 gr-qc math-phmath.MP

Delay Equations and Radiation Damping

classification gr-qc math-phmath.MP
keywords equationsdelayeffectsmotionretardationmanifoldradiationsmall
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Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we identify this invariant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not contained in the local equations of motion.

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    gr-qc 2013-10 unverdicted novelty 2.0

    A review of the MPM-PN approximation scheme that yields equations of motion to 4PN order and gravitational waveforms and fluxes to 4.5PN order for compact binary systems.