Classical n-body scattering with long-range potentials

Fejoz J, Knauf A, Montgomery R (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Nonlinearity Institute of Physics: Hybrid Open Access

Book Volume: 34

Pages Range: 8017-8054

Journal Issue: 11

DOI: 10.1088/1361-6544/ac288d

Abstract

We consider the scattering of n classical particles interacting via pair potentials which are assumed to be 'long-range', i.e. of order O(r(-alpha)) r tends to infinity, for some alpha > 0. We define and focus on the 'free region', the set of states leading to well-defined and well-separated final states at infinity. As a first step, we prove the existence of an explicit, global surface of section for the free region. This surface of section allows us to prove the smoothness of the map sending a point to its final state and to establish a forward conjugacy between the n-body dynamics and free dynamics.

Authors with CRIS profile

Andreas Knauf Lehrstuhl für Mathematik (Mathematische Physik)

Involved external institutions

University of Paris 9 - Paris-Dauphine / Université Paris 9 Paris-Dauphine FR France (FR) University of California Santa Cruz US United States (USA) (US)

How to cite

APA:

Fejoz, J., Knauf, A., & Montgomery, R. (2021). Classical n-body scattering with long-range potentials. Nonlinearity, 34(11), 8017-8054. https://doi.org/10.1088/1361-6544/ac288d

MLA:

Fejoz, Jacques, Andreas Knauf, and Richard Montgomery. "Classical n-body scattering with long-range potentials." Nonlinearity 34.11 (2021): 8017-8054.

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