*Lecture on Tuesday, September 4 has been cancelled due to approaching typhoon "Jebi", and two lectures will take place instead on Wednesday, September 5 as follows.
Top Global Course Special Lectures by Prof. Urs Frauenfelder (Augsburg University) will take place as follows:
- Course Title
- Top Global Course Special Lectures 4
- Date & Time
- September 3 to 7, 2018 (5 lectures)
- Monday, September 3, 13:30-15:30
- Wednesday, September 5, 10:00-12:00 / 13:30-15:30 (Rescheduled lecture for Sep 4)
- Thursday, September 6, 10:00-12:00
- Friday, September 7, 10:00-12:00
- 127 Conference room, Faculty of Science Bldg. #3, Kyoto University
- The restricted three-body problem and holomorphic curves
- 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.
- This series of lectures will be video-recorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.