Urs Frauenfelder教授 スーパーグローバルコース数学特別講義

Urs Frauenfelder教授(Augsburg University)によるスーパーグローバルコース数学特別講義を下記の要領で行います。

スーパーグローバルコース 数学特別講義4
日 時
2018年9月3日〜9月7日 全5回
  • 9月3日(月) 13:30〜15:30
  • 9月4日(火) 10:00〜12:00
  • 9月5日(水) 10:00〜12:00
  • 9月6日(木) 10:00〜12:00
  • 9月7日(金) 10:00〜12:00
場 所
京都大学理学部3号館 127大会議室
題 目
The restricted three-body problem and holomorphic curves
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.
言 語
備 考