dc.contributor.author |
Barrett, D.I.
|
|
dc.contributor.author |
Biggs, Rory
|
|
dc.contributor.author |
Remsing, C.C.
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|
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) |
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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 |