The Adler-van Moerbeke integrable case. Visualization of bifurcations of Liouville tori

DOI10.20537/vm170404zbMath1401.70006OpenAlexW2794039209MaRDI QIDQ4961695

Sergei V. Sokolov

Publication date: 25 October 2018

Published in: Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vuu606

zbMATH Keywords

bifurcation diagramintegrable Hamiltonian systemsbifurcations of Liouville tori

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Motion of a rigid body with a fixed point (70E17) Motion of the gyroscope (70E05)

Cites Work

• New invariant relations for the generalized two-field gyrostat
• Bi-Hamiltonian structures and singularities of integrable systems
• Singularities of bi-Hamiltonian systems
• A new integrable case of the motion of the 4-dimensional rigid body
• Compatible Poisson brackets on Lie algebras
• The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram
• Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras
• Singularities of Integrable Systems and Algebraic Curves
• Geometry of translations of invariants on semisimple Lie algebras
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