The Sokolov case, integrable Kirchhoff elasticae, and genus 2 theta functions via discriminantly separable polynomials

DOI10.1134/S0081543814060133zbMath1322.37026MaRDI QIDQ2514593

Katarina Kukić, Vladimir Dragović

Publication date: 3 February 2015

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

integrable systemstheta functionsKowalevski topKirchhoff systemSokolov system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Elliptic curves (14H52) Relationships between algebraic curves and integrable systems (14H70) Integrable cases of motion in rigid body dynamics (70E40)

Related Items (5)

Two-valued groups, Kummer varieties, and integrable billiards ⋮ Topological atlas of the Kowalevski-Sokolov top ⋮ Some recent generalizations of the classical rigid body systems ⋮ Caustics of Poncelet polygons and classical extremal polynomials ⋮ Discriminantly separable polynomials and the generalized Kowalevski top

Cites Work

• Geometrization and generalization of the Kowalevski top
• A new integrable case for the Kirchhoff equation
• Two-valued groups, Kummer varieties, and integrable billiards
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Integrable Hamiltonian systems on Lie groups: Kowalewski type
• New examples of systems of the Kowalevski type
• Systems of Kowalevski type and discriminantly separable polynomials
• Discriminantly separable polynomials and quad-equations
• Kowalewski's top on the Lie algebras o(4), e(3), and o(3,1)
• Poisson maps and integrable deformations of the Kowalevski top
• Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups
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