The generalized Hénon-Heiles system, abelian surfaces and algebraic complete integrability

DOI10.1016/S0034-4877(01)90002-3zbMath1054.37038MaRDI QIDQ5933506

Ahmed Lesfari

Publication date: 26 March 2002

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Riemann surfacesintegrable systemsAbelian varietesPrym varietes

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Jacobians, Prym varieties (14H40) Relationships between algebraic curves and integrable systems (14H70)

Related Items (1)

A Connection Between Geometry and Dynamical Systems

Cites Work

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• Bifurcations of invariant manifolds in the generalized Hénon-Heiles system
• The algebraic integrability of geodesic flow on SO(4)
• The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs
• Completely integrable systems: Jacobi's heritage
• On affine surface that can be completed by a smooth curve
• Geodesic flow on \(\text{SO}(4)\), Kac-Moody Lie algebra and singularities in the complex \(t\)-plane
• Abelian surfaces and Kowalewski's top

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