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SUMMARY:AG Mathematische Physik\, Manuel Quaschner (FAU): Noncollision
  singularities with external forces
UID:5c127f72-3832-7841-8dfb-efc6454f217e
DESCRIPTION:Manuel Quaschner (FAU) Noncollision singularities with ext
 ernal forces Abstract: The existence of noncollision singularities in 
 the $n$-body problem was already conjectured by Painlevé in 1895. Eve
 n before the existence was proven in the 1990s\, the question came up\
 , whether the set of all initial conditions leading to noncollision si
 ngularities is a set of measure 0. A first result of this kind was pro
 ven for $n=4$ particles in $dgeq 2$ dimensions by Saari (1977). Using 
 the so called Poincaré surface method\, Fleischer (2018) could improv
 e this for $n=4$ particles in $d geq 2$ dimensions by extending the re
 sult to a wider class of potentials. But the problem is still open for
  more than four particles. After an overview of these works\, we add s
 ome sufficiently small external forces to the well understood case of 
 $n=4$ particles. In order to apply the Poincaré surface method\, we n
 eed to prove good estimates on the shape of the orbits\, which are clo
 se to the movement on a straight line. In the end we will show how one
  could use this results to prove the improbability of larger systems t
 hat can be suitably decomposed into diverging systems of up to four pa
 rticles each.
DTSTART:20220210T151500Z
DTEND:20220210T170000Z
LOCATION:Übung 1 / 01.250-128\, Erlangen
DTSTAMP:20261011T095706Z
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