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Exactly Solvable and Integrable Systems

arXiv:solv-int/9402003 (solv-int)
[Submitted on 18 Feb 1994]

Title:Multi-Hamiltonian formulation for a class of degenerate completely integrable systems

Authors:Peter Bueken (Katholieke Universiteit Leuven)
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Abstract: Generalizing a construction of P. Vanhaecke, we introduce a large class of degenerate (i.e., associated to a degenerate Poisson bracket) completely integrable systems on (a dense subset of) the space $\R^{2d+n+1}$, called the generalized master systems. It turns out that certain generalized master systems (with different Poisson brackets and different Hamiltonians) determine the same Hamiltonian vector fields (and are therefore different descriptions of the same Hamiltonian system), and that the Poisson brackets of these systems are compatible. Consequently, our class of generalized master systems actually consists of a (smaller) class of completely integrable systems, and our construction yields a multi-Hamiltonian structure for these systems. As an application, we construct a multi-Hamiltonian structure for the so-called master systems introduced by D. Mumford.
Comments: 25 pages, plain TeX, necessary macros included
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:solv-int/9402003
  (or arXiv:solv-int/9402003v1 for this version)
  https://doi.org/10.48550/arXiv.solv-int/9402003

Submission history

From: [view email]
[v1] Fri, 18 Feb 1994 12:28:56 UTC (16 KB)
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