Geometric Models for Lie–Hamilton Systems on ℝ2
| Autor: | Javier de Lucas, Julia Lange |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Transitive relation
Pure mathematics integral system 010308 nuclear & particles physics General Mathematics lcsh:Mathematics Lie system Lie–Hamilton system Quotient space (linear algebra) lcsh:QA1-939 01 natural sciences symplectic geometry Poisson manifold 0103 physical sciences Lie algebra Computer Science (miscellaneous) Computer Science::Programming Languages Lie algebra of vector fields 010306 general physics Engineering (miscellaneous) Bivector superposition rule Mathematics Symplectic geometry |
| Zdroj: | Mathematics Volume 7 Issue 11 Mathematics, Vol 7, Iss 11, p 1053 (2019) |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math7111053 |
| Popis: | This paper provides a geometric description for Lie&ndash Hamilton systems on R 2 with locally transitive Vessiot&ndash Guldberg Lie algebras through two types of geometric models. The first one is the restriction of a class of Lie&ndash Hamilton systems on the dual of a Lie algebra to even-dimensional symplectic leaves relative to the Kirillov-Kostant-Souriau bracket. The second is a projection onto a quotient space of an automorphic Lie&ndash Hamilton system relative to a naturally defined Poisson structure or, more generally, an automorphic Lie system with a compatible bivector field. These models give a natural framework for the analysis of Lie&ndash Hamilton systems on R 2 while retrieving known results in a natural manner. Our methods may be extended to study Lie&ndash Hamilton systems on higher-dimensional manifolds and provide new approaches to Lie systems admitting compatible geometric structures. |
| Databáze: | OpenAIRE |
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