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Utah State University

1. Seegmiller, Patrick. Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie Algebra.

Degree: MS, Mathematics and Statistics, 2015, Utah State University

URL: https://digitalcommons.usu.edu/etd/4699

The Toda flow is a Hamiltonian system which evolves on the dual of the Borel subalgebra of a complex Lie algebra g. The dual of the Borel subalgebra can be identified with an affine subspace of its negative plus the element given by the sum of the simple root vectors in g. The system has been proven completely integrable in the Liouville sense on a generic coadjoint orbit for the Borel subgroup. This paper gives a verification of integrability of the Toda flow on classical simple Lie algebras and describes a method for the construction of a complete collection of integrals of motion for each. After this description, an implementation of the outlined procedures is given in the Maple programming environment, together with explicit examples, demonstrating both the accuracy of the procedure and the efficacy of the Maple programming code.
*Advisors/Committee Members: Zhaohu Nie, ;.*

Subjects/Keywords: Algebra; Flow; Lie; Toda; Mathematics; Physics

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APA (6^{th} Edition):

Seegmiller, P. (2015). Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie Algebra. (Masters Thesis). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/4699

Chicago Manual of Style (16^{th} Edition):

Seegmiller, Patrick. “Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie Algebra.” 2015. Masters Thesis, Utah State University. Accessed January 26, 2020. https://digitalcommons.usu.edu/etd/4699.

MLA Handbook (7^{th} Edition):

Seegmiller, Patrick. “Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie Algebra.” 2015. Web. 26 Jan 2020.

Vancouver:

Seegmiller P. Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie Algebra. [Internet] [Masters thesis]. Utah State University; 2015. [cited 2020 Jan 26]. Available from: https://digitalcommons.usu.edu/etd/4699.

Council of Science Editors:

Seegmiller P. Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie Algebra. [Masters Thesis]. Utah State University; 2015. Available from: https://digitalcommons.usu.edu/etd/4699