Journal of Shanghai Jiaotong University (Science)

, Volume 23, Issue 1, pp 146–157 | Cite as

Focal Points at Infinity for Short-Range Scattering Trajectories

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Abstract

Classical scattering trajectories are known to form a Lagrangian manifold in euclidean phase space, which allows the classification of local focal points for sufficiently small dimensions. For the case of a short-range potential, we show that the natural description of focal points at infinity is a Lagrangian manifold in the cotangent bundle of the sphere and establish the relationship between focal points at infinity and the projection singularities of that manifold.

Key words

Lagrangian manifold classical scattering theory short-range potential 

CLC number

O 17 

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Copyright information

© Shanghai Jiaotong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Michigan - Shanghai Jiao Tong University Joint InstituteShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Institute for MathematicsUniversity of PotsdamPotsdamGermany

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