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Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller
Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The Toda flow is a generalization of a dynamical system describing the interaction of particles in a one-dimensional crystal. The concepts and energy and conservation are prominent in the study of dynamical systems, and quantities which remain the same over the evolution of a system provide valuable insights into the system’s behavior. In the realm of mathematics these quantities are called first integrals, or integrals of motion. This paper provides a background for study of the Toda flow, a verification of its integrability, and programming code for finding these quantities which remain unchanged over the evolution of the system.