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.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-5740 |
| Date | 01 May 2015 |
| Creators | Seegmiller, Patrick |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu). |
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