Direct construction of a bi-hamiltonian structure for cubic hÉnon-heiles systems

Author First name, Last name, Institution

Nicola Sottocornola

Document Type

Article

Source of Publication

Journal of Geometry and Symmetry in Physics

Publication Date

1-1-2020

Abstract

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.

DOI Link

10.7546/jgsp-57-2020-99-109

ISSN

1312-5192

Publisher

Bulgarska Akademiya na Naukite

Volume

57

First Page

99

Last Page

109

Disciplines

Physical Sciences and Mathematics

Keywords

Integrable systems, Integration in quadratures, Separation of variables

Scopus ID

85099684566

Recommended Citation

Sottocornola, Nicola, "Direct construction of a bi-hamiltonian structure for cubic hÉnon-heiles systems" (2020). All Works. 1280.
https://zuscholars.zu.ac.ae/works/1280

Indexed in Scopus

yes

Open Access

no