The restricted three-body problem and holomorphic curves

2018/09/03 月 13:30 - 15:30
2018/09/05 水 10:00 - 12:00
2018/09/05 水 13:30 - 15:30
2018/09/06 木 10:00 - 12:00
2018/09/07 金 10:00 - 12:00
Urs Frauenfelder
Augsburg University

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)