Geometric Models for Lie–Hamilton Systems on ? 2

Julia Lange and Javier de Lucas
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Julia Lange: Department of Mathematical Methods in Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
Javier de Lucas: Department of Mathematical Methods in Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland

Mathematics, 2019, vol. 7, issue 11, 1-17

Abstract: This paper provides a geometric description for Lie–Hamilton systems on R 2 with locally transitive Vessiot–Guldberg Lie algebras through two types of geometric models. The first one is the restriction of a class of Lie–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–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–Hamilton systems on R 2 while retrieving known results in a natural manner. Our methods may be extended to study Lie–Hamilton systems on higher-dimensional manifolds and provide new approaches to Lie systems admitting compatible geometric structures.

Keywords: Lie system; superposition rule; Lie–Hamilton system; integral system; symplectic geometry; Lie algebra of vector fields (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:11:p:1053-:d:283395

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