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SUMMARY:Renato Calleja (UNAM\, Mexico)
DTSTART:20200811T140000Z
DTEND:20200811T150000Z
DTSTAMP:20260423T024549Z
UID:CRM-CAMP/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/7/"
 >Torus knot choreographies in the n-body problem</a>\nby Renato Calleja (U
 NAM\, Mexico) as part of CRM CAMP (Computer-Assisted Mathematical Proofs) 
 in Nonlinear Analysis\n\n\nAbstract\nn-body choreographies are periodic so
 lutions to the n-body equations in which equal masses chase each other aro
 und a fixed closed curve. In this talk I will present a systematic approac
 h for proving the existence of spatial choreographies in the gravitational
  body problem with the help of the digital computer. These arise from the 
 polygonal system of bodies in a rotating frame of reference. In rotating c
 oordinates\, after exploiting the symmetries\, the equation of a choreogra
 phic configuration is reduced to a delay differential equation (DDE) descr
 ibing the position and velocity of a single body. We prove that a dense se
 t of Lyapunov orbits\, with frequencies satisfying a Diophantine equation\
 , correspond to choreographies.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/7/
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