Abstract
Asymptotic properties of solutions ofN-body classical equations of motion are studied.
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[A] Agmon, S.: Lectures on the exponential decay of solutions of second order elliptic equations. Princeton, NJ: Princeton University Press 1982
[De1] Dereziński, J.: A new proof of the propagation theorem forN-body quantum systems. Commun. Math. Phys.122, 203–231 (1989)
[De2] Dereziński, J.: Algebraic approach to theN-body long range scattering. Rev. Math. Phys.3, 1–62 (1991)
[De3] Dereziński, J.: Asymptotic completeness of long rangeN-body quantum systems. Preprint, Ecole Polytechnique 1991
[E1] Enss, V.: Quantum scattering theory of two- and three-body systems with potentials of short and long range. In: Schrödinger operators, Graffi, S. (ed.): Lect. Notes in Math., Vol. 1159. Berlin, Heidelberg, New York: Springer 1985
[E2] Enss, V.: Two-and three-body quantum scattering: Completeness revisited. In: Proceedings of the “Conference on partial differential equations”. Leipzig: Reubner-Texte zur Mathematik, Schulze, B.-W. (ed.), 1989
[Graf] Graf, G.M.: Asymptotic completeness forN-body short range systems: a new proof. Commun. Math. Phys.132, 73–101 (1990)
[He] Herbst, I.: Classical scattering with long range forces. Commun. Math. Phys.35, 193–214 (1974)
[Hö] Hörmander, L.: The analysis of linear partial differential operators, Vols. 1, 2, 1983 and Vols. 3, 4, 1985. Berlin, Heidelberg, New York: Springer
[Hu] Hunziger, W.: TheS-matrix in classical mechanics. Commun. Math. Phys.8, 282–299 (1968)
[IKi] Isozaki, H., Kitada, H.: Modified wave operators with time independent modifiers. J. Fac. Sci. Univ. Tokyo, Sec. 1A,32, 77–104 (1985)
[Pe] Perry, P.: Scattering theory by the Enss method. London: Harward Academic 1983
[RS] Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. III: Scattering theory, 1979 and Vol. IV: Analysis of Operators, 1978. London: Academic Press
[Sig] Sigal, I.M.: On the long range scattering. Duke Math. J.60, 473–492 (1990)
[SigSof1] Sigal, I.M., Soffer, A.: TheN-particle scattering problem: Asymptotic completeness for short range systems. Anal. Math.125, 35–108 (1987)
[SigSof2] Sigal, I.M., Soffer, A.: Local decay and velocity bounds. Preprint, Princeton University 1988
[SigSof3] Sigal, I.M., Soffer, A.: Long range many body scattering. Asymptotic clustering for Coulomb type potentials. Invent. Math.99, 115–143 (1990)
[SigSof4] Sigal, I.M., Soffer, A.: Asymptotic completeness for four-body Coulomb systems. Preprint 1991
[Sim] Simon, B.: Wave operators for classical particle scattering. Commun. Math. Phys.23, 37–48 (1971)
[Ya] Yafaev, D.R.: Radiation conditions and scattering theory for three-particle Hamiltonians. Preprint, Univ. de Nantes 1991
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Communicated by B. Simon
Supported in part by a grant from the Ministry of Education of Poland
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Dereziński, J. Large time behavior of classicalN-body systems. Commun.Math. Phys. 148, 503–520 (1992). https://doi.org/10.1007/BF02096547
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DOI: https://doi.org/10.1007/BF02096547