The restricted three-body problem and holomorphic curves

開催日時: 
2018/09/03 Mon 13:30 - 15:30
2018/09/05 Wed 10:00 - 12:00
2018/09/05 Wed 13:30 - 15:30
2018/09/06 Thu 10:00 - 12:00
2018/09/07 Fri 10:00 - 12:00
場所: 
3号館127大会議室
講演者: 
Urs Frauenfelder
講演者所属: 
Augsburg University
概要: 

The restricted three-body problem describes the dynamics of a massless particle attracted by two masses. For example the massless particle could be the moon and the masses earth and sun, or a satellite attracted by the earth and moon, or a planet attracted by two stars in a double star system. Different from the two-body problem which is completely integrable the dynamics of the restricted three-body problem has chaotic behaviour.

A global surface of section reduces the complexity of the dynamics by one dimension. More than hundred years ago Birkhoff made a conjecture about the existence of a global surface of section for the restricted three-body problem. Although the question about existence of a global surface of section is a question about all orbits, holomorphic curves allow to reduce the Birkhoff conjecture to questions involving periodic orbits only.

In the lecture I explain the theory of holomorphic finite energy planes, what they imply for the Birkhoff conjecture, and what challenges remain to be done to prove the conjecture.

*台風21号の接近に伴い、9月4日(火) 10:00〜の講義を取り止め、9月5日(水)に2回分の講義を行います。(9月3日追記)

*本講義は録画し、Web上で公開します。講義室前方はカメラに写る場合がありますので、予めご了承下さい。

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