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Consecutive Rosochatius deformations of the Garnier system and the Hénon-Heiles system. (English) Zbl 1449.37039

Summary: An algorithm of constructing infinitely many symplectic realizations of generalized sl(2) Gaudin magnet is proposed. Based on this algorithm, the consecutive Rosochatius deformations of integrable Hamiltonian systems are presented. As examples, the consecutive Rosochatius deformations of the Garnier system and the Hénon-Heiles system as well as their Lax representations, are obtained.

MSC:

37J37 Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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