%0 Journal Article
%T Geometric Models for Lie每Hamilton Systems on ˋ2
%J Mathematics | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/math7111053
%X This paper provides a geometric description for Lie每Hamilton systems on R 2 with locally transitive Vessiot每Guldberg Lie algebras through two types of geometric models. The first one is the restriction of a class of Lie每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每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每Hamilton systems on R 2 while retrieving known results in a natural manner. Our methods may be extended to study Lie每Hamilton systems on higher-dimensional manifolds and provide new approaches to Lie systems admitting compatible geometric structures. View Full-Tex
%U https://www.mdpi.com/2227-7390/7/11/1053