Authors: Fedorov, Yuri
Jovanović, Božidar 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Continuous and discrete neumann systems on stiefel varieties as matrix generalizations of the jacobi-mumford systems
Journal: Discrete and Continuous Dynamical Systems- Series A
Volume: 41
Issue: 6
First page: 2559
Last page: 2599
Issue Date: 1-Jun-2021
Rank: ~M21
ISSN: 1078-0947
DOI: 10.3934/dcds.2020375
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties Vn,r. The systems are integrable in the non-commutative sense, and by applying a 2r × 2r-Lax representation, we show that generic complex invariant manifolds are open subsets of affine Prym varieties on which the complex flow is linear. The characteristics of the varieties and the direction of the flow are calculated explicitly. Next, we construct a family of multi-valued integrable discretizations of the Neumann systems and describe them as translations on the Prym varieties, which are written explicitly in terms of divisors of points on the spectral curve.
Keywords: Integrable systems | Invariant tori | Multi-valued mappings | Prym varieties | Spectral curves
Publisher: American Institute of Mathematical Sciences

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