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Explore the mathematical classification of braids arising from 3-body motions along Lissajous curves on the plane in this 56-minute research lecture by Hiroaki Nakamura from Osaka University. Delve into the combinatorial and arithmetic properties of these special braids through multiple mathematical perspectives including associated continued fractions, cutting sequences of checkered Farey tessellation, and symbolic frieze patterns. Learn about the collaborative research findings developed with Eiko Kin and Hiroyuki Ogawa that illuminate the deep connections between geometric motion, braid theory, and number theory. Discover how Lissajous curves, which describe the motion of particles in two-dimensional harmonic oscillators, generate intricate braided structures when extended to three-body systems, and understand the mathematical tools used to analyze and classify these complex topological objects.
