*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

Venue

127 Conference room, Faculty of Science Bldg. #3, Kyoto University

Title

The restricted three-body problem and holomorphic curves

Abstract

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.

Language

English

Note

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.