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Explore the first 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 this system differs from the simpler two-body problem through its chaotic behavior. Examine Birkhoff's century-old conjecture about global surface sections and discover how holomorphic curves can simplify this complex mathematical challenge by focusing on periodic orbits. Understand the theory of holomorphic finite energy planes, their implications for the Birkhoff conjecture, and the remaining challenges in proving this mathematical proposition. Originally presented on September 3, 2018, at Kyoto University's Graduate School of Science.
