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Exponential stability of Euler integral in the three--body problem

Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018

October 11, 2018 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Gabriella Pinzari (Università di Padova)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords
  • Three--body problem

  • Normal form theory

  • Two--centre problem

  • Euler Integral

  • Prediction of collisions

  • canonical coordinates

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

16-Pinzari

Abstract

The first integral characteristic of the fixed two--centre problem is proven to be an approximate integral (in the sense of N.N.Nekhorossev) to the three--body problem, at least if the masses are very different and the particles are constrained on a plane. The proof uses a new normal form result, carefully designed around the degeneracies of the problem, and a new study of the phase portrait of the unperturbed problem. Applications to the prediction of collisions between the two minor bodies are shown.

Supplements
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Video/Audio Files

16-Pinzari

H.264 Video 16-Pinzari.mp4 158 MB video/mp4 Download
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