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DTSTAMP:20260403T230833Z
UID:62457a4f490aa733121096@ist.ac.at
DTSTART:20220411T151500
DTEND:20220411T161500
DESCRIPTION:Speaker: Marcel Guardia Munarriz\nhosted by Kaloshin Group\nAbs
 tract: Consider the three body problem with positive masses $m_0$\, $m_1$ 
 and $m_2$. In 1922 Chazy classified the possible final motions the three b
 odies may possess\, that is the behaviors the bodies may have when time te
 nds to infinity. One of them are what is known as oscillatory motions\, th
 at is\, solutions of the three body problem such that the liminf (as time 
 tends to infinity) of the relative positions between bodies is finite wher
 eas the limsup is infinite. That is\, solutions for which the bodies keep 
 oscillating between an increasingly large separation and getting closer to
 gether. The first result of existence of oscillatory motions was provided 
 by Sitnikov for a a Restricted Three Body Problem\, called nowadays Sitnki
 kov model. His result has been extended to several Celestial Mechanics mod
 els but always with rather strong assumptions on the values of the masses.
 In this talk I will explain how to construct oscillatory motions for the t
 hree body problem for any values $m_0$\, $m_1$ and $m_2$ (except for the c
 ase of three equal masses). The proof relies on the construction of hyperb
 olic invariant sets whose dynamics is conjugated to that of the shift of i
 nfinite symbols (i.e. symbolic dynamics). That is\, we construct invariant
  sets for the three body problem with chaotic dynamics\, which moreover co
 ntain oscillatory motions. This is a joint work with Pau Martin\, Jaime Pa
 radela and Tere M. Seara.
LOCATION:Mondi Seminar Room 2\, Central Building\, ISTA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Marcel Guardia Munarriz: Oscillatory motions and symbolic dynamics 
 in the three body problem
URL:https://talks-calendar.ista.ac.at/events/3687
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