99-1 Kunze M., Spohn H.

Radiation Reaction and Center Manifolds (78K, LaTeX) Jan 2, 99

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Abstract. 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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