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On some quadratic Hamilton-Poisson systems
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer Science+Business Media B.V., part of Springer Nature
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-017-0140-3
- Publisher site
- See Article on Publisher Site
Abstract
We consider equivalence, stability and integration of quadratic Hamilton–Poisson systems on the semi-Euclidean Lie–Poisson space se ( 1 , 1 ) − ∗ $\mathfrak{se}(1,1)^{*}_{-}$ . The inhomogeneous positive semidefinite systems are classified (up to affine isomorphism); there are 16 normal forms. For each normal form, we compute the symmetry group and determine the Lyapunov stability nature of the equilibria. Explicit expressions for the integral curves of a subclass of the systems are found. Finally, we identify several basic invariants of quadratic Hamilton–Poisson systems.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Nov 24, 2017