Quadratic Hamilton–Poisson systems on se(1,1)∗− : the Inhomogeneous case
| dc.contributor.author | Barrett, D.I. | |
| dc.contributor.author | Biggs, Rory | |
| dc.contributor.author | Remsing, C.C. | |
| dc.date.accessioned | 2018-09-20T13:41:05Z | |
| dc.date.issued | 2018-04 | |
| dc.description.abstract | We consider equivalence, stability and integration of quadratic Hamilton–Poisson systems on the semi-Euclidean Lie–Poisson space 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. | en_ZA |
| dc.description.department | Mathematics and Applied Mathematics | en_ZA |
| dc.description.embargo | 2019-04-01 | |
| dc.description.librarian | hj2018 | en_ZA |
| dc.description.sponsorship | This research was supported in part by the European Union’s Seventh Framework Programme (FP7/2007-2013, grant no. 317721). The first two authors would also like to acknowledge the financial support of the National Research Foundation (NRF-DAAD) and Rhodes University towards this research. Additionally, the second author acknowledges the financial support of the Claude Leon Foundation. | en_ZA |
| dc.description.uri | http://link.springer.com/journal/10440 | en_ZA |
| dc.identifier.citation | Barrett, D.I., Biggs, R. & Remsing, C.C. Quadratic Hamilton–Poisson Systems on se(1,1)∗−: The Inhomogeneous Case. Acta Applicandae Mathematicae (2018) 154: 189-230. https://doi.org/10.1007/s10440-017-0140-3. | en_ZA |
| dc.identifier.issn | 0167-8019 (print) | |
| dc.identifier.issn | 1572-9036 (online) | |
| dc.identifier.other | 10.1007/s10440-017-0140-3 | |
| dc.identifier.uri | http://hdl.handle.net/2263/66610 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | Springer | en_ZA |
| dc.rights | © Springer Science+Business Media B.V., part of Springer Nature 2017. The original publication is available at : http://link.springer.comjournal/10440. | en_ZA |
| dc.subject | Hamilton–Poisson system | en_ZA |
| dc.subject | Lie–Poisson space | en_ZA |
| dc.subject | Lyapunov stability | en_ZA |
| dc.subject | Poisson equation | en_ZA |
| dc.subject | Euclidean | en_ZA |
| dc.subject | Hamiltons | en_ZA |
| dc.subject | Integral curves | en_ZA |
| dc.subject | Normal form | en_ZA |
| dc.subject | Positive semidefinite | en_ZA |
| dc.subject | Symmetry groups | en_ZA |
| dc.subject | System stability | en_ZA |
| dc.title | Quadratic Hamilton–Poisson systems on se(1,1)∗− : the Inhomogeneous case | en_ZA |
| dc.type | Postprint Article | en_ZA |