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Complete Integrability And Discretization Of Euler Top And Manakov Top, Austin Marstaller
Complete Integrability And Discretization Of Euler Top And Manakov Top, Austin Marstaller
Theses and Dissertations
The Euler top is a completely integrable system with physical system implications and the Manakov top is its four-dimensional extension. We are concerned about their complete integrability and the preservation of this property under a specific discretization known as the Hirota-Kimura Discretization. Surprisingly, it is not guaranteed that under any discretization the conserved quantities are preserved and therefore they must be discovered. In this work we construct the Poisson bracket and Lax pair for each system and provide the Lie algebra background needed to do such such constructions.