Integrable systems and linear flows on tori
by Gus Schrader
Abstract: The theory of classical integrable systems has rich topological and geometric content. In this talk, I will discuss the Liouville-Arnold definition of a completely integrable Hamiltonian system, and explain how the flow of such a system corresponds to the linear motion of a point on a
(real) torus. I will then consider the concept of Lax integrablility, and explain how Lax equations with spectral parameter describe the linear motion of a point on a (complex) torus, which is the Jacobian of a compact Riemann surface.
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