## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Quadratic Hamilton-Poisson Systems on $\mathfrak{so}^*_{-}(3)$: Classification and Integration

#### Abstract

We classify, under affine equivalence, the quadratic Hamilton-Poisson systems on the Lie-Poisson space $\mathfrak{so}^*_{-}(3)$. For the simplest strictly inhomogeneous quadratic system, we find explicit expressions for the integral curves in terms of Jacobi elliptic functions.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436815701

Digital Object Identifier
doi:10.7546/giq-15-2014-55-66

Mathematical Reviews number (MathSciNet)
MR3287748

Zentralblatt MATH identifier
1315.37030

#### Citation

Adams, Ross M.; Biggs, Rory; Remsing, Claudiu C. Quadratic Hamilton-Poisson Systems on $\mathfrak{so}^*_{-}(3)$: Classification and Integration. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 55--66, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-55-66. https://projecteuclid.org/euclid.pgiq/1436815701