Xia, Baoqiang; Zhou, Ruguang Consecutive Rosochatius deformations of the Garnier system and the Hénon-Heiles system. (English) Zbl 1449.37039 Abstr. Appl. Anal. 2014, Article ID 275450, 8 p. (2014). 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 Keywords:sl(2) Gaudin magnet; Rosochatius deformations; Garnier system; Hénon-Heiles system × Cite Format Result Cite Review PDF Full Text: DOI OA License References: [1] Rosochatius, E., Uber die Bewegung eines Punktes, [Ph.D. dissertation] (1877), University of Gotingen · JFM 09.0651.02 [2] Neumann, C., De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur, Journal für die Reine und Angewandte Mathematik, 56, 46-63 (1859) · ERAM 056.1472cj · doi:10.1515/crll.1859.56.46 [3] Moser, J., Geometry of quadrics and spectral theory, The Chern Symposium 1979, 147-188 (1980), New York, NY, USA: Springer, New York, NY, USA · Zbl 0455.58018 · doi:10.1007/978-1-4613-8109-9_7 [4] Adams, M. 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