Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves

V. M. Buchstaber   ; A. V. Mikhailov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 4, pp. 587-652

Résumé

This survey is devoted to integrable polynomial Hamiltonian systems associated with symmetric powers of plane algebraic curves. We focus our attention on the relations (discovered by the authors) between the Stäckel systems, Novikov's equations for the $g$th stationary Korteweg–de Vries hierarchy, the Dubrovin–Novikov coordinates on the universal bundle of Jacobians of hyperelliptic curves, and new systems obtained by considering the symmetric powers of curves when the power is not equal to the genus of the curve. Bibliography: 52 titles.

Détail

Keywords: polynomial Hamiltonian systems, Stäckel systems, Korteweg–de Vries hierarchy, symmetric powers of curves, Abelian functions, systems of hydrodynamical type.

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