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Explore the third lecture in a series on the restricted three-body problem and holomorphic curves, delivered by Professor Urs Frauenfelder from Augsburg University. Delve into the complex dynamics of a massless particle influenced by two masses, such as the moon's interaction with Earth and Sun, or a satellite affected by Earth and moon. Learn how the restricted three-body problem exhibits chaotic behavior, unlike the completely integrable two-body problem. Examine Birkhoff's century-old conjecture about global surface of section existence and discover how holomorphic curves can simplify this complex problem to focus on periodic orbits. Master the theory of holomorphic finite energy planes, understand their implications for the Birkhoff conjecture, and investigate the remaining challenges in proving this mathematical proposition. Originally presented on September 3-7, 2018, at Kyoto University's Graduate School of Science.
