Direct construction of a bi-hamiltonian structure for cubic hÉnon-heiles systems
Source of Publication
Journal of Geometry and Symmetry in Physics
The problem of separating variables in integrable Hamiltonian systems has been extensively studied in the last decades. A recent approach is based on the so called Kowalewski's Conditions used to characterized a Control Matrix M whose eigenvalues give the desired coordinates. In this paper we calculate directly a second compatible Hamiltonian structure for the cubic Hénon-Heiles systems and in this way we obtain the separation variables as the eigenvalues of a recursion operator N. Finally we re-obtain the Control Matrix M from N. © 2020 Bulgarian Academy of Sciences. All rights reserved.
Bulgarska Akademiya na Naukite
Physical Sciences and Mathematics
Integrable systems; Integration in quadratures; Separation of variables
Sottocornola, Nicola, "Direct construction of a bi-hamiltonian structure for cubic hÉnon-heiles systems" (2020). All Works. 1280.
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