It is known that finite gap potentials of Hill's equation y" + q(τ)y = Ey can be obtained as solutions of an integrable dynamical system: uncoupled harmonic oscillators constrained to move on the unit sphere in configuration space--The Neumann System. This Dissertation systematizes and generalizes this result. First, the theory of Baker-Akhiezer functions is placed on a solid mathematical foundation. Guided by the theory of Baker-Akhiezer functions and Riemann surfaces, trace formulas, particle systems, constraints, integrals and Lax pairs are systematically constructed for the particle system of the ℓ x ℓ matrix differential operator of order n.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/184658 |
| Date | January 1982 |
| Creators | SCHILLING, RANDOLPH JAMES. |
| Contributors | Flaschka, H. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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