Radiation Reaction and Center Manifolds

Details Radiation Reaction and Center Manifolds Radiation Reaction and Center Manifolds

1999-01-12

arxiv.org/abs/math-ph/9901004v1

Physics

Mathematical Physics

Scientific paper

We study the effective dynamics of a mechanical particle coupled to a wave field and subject to the slowly varying potential $V(\eps q)$ with $\eps$ small. To lowest order in $\eps$ the motion of the particle is governed by an effective Hamiltonian. In the next order one obtains ``dissipative'' terms which describe the radiation reaction. We establish that this dissipative dynamics has a center manifold which is repulsive in the normal direction and which is global, in the sense that for given data and sufficiently small $\eps$ the solution stays on the center manifold forever. We prove that the solution of the full system is well approximated by the effective dissipative dynamics on its center manifold.

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