Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems
Differential Geometry
2025-03-27 v2 Mathematical Physics
math.MP
Abstract
In 1986, Albert proposed a Marsden-Weinstein reduction process for cosymplectic structures. In this paper, we present the limitations of this theory in the application of the reduction of symmetric time-dependent Hamiltonian systems. As a consequence, we conclude that cosymplectic geometry is not appropriate for this reduction. Motived for this fact, we replace cosymplectic structures by more general structures: mechanical presymplectic structures. Then, we develop Marsden-Weinstein reduction for this kind of structures and we apply this theory to interesting examples of time-dependent Hamiltonian systems for which Albert's reduction method doesn't work.
Keywords
Cite
@article{arxiv.2411.11997,
title = {Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems},
author = {I. Gutierrez-Sagredo and D. Iglesias Ponte and J. C. Marrero and E. Padrón},
journal= {arXiv preprint arXiv:2411.11997},
year = {2025}
}
Comments
24 pages, 2 figures; References added