PreprintCC BY 4.0arXiv
Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal ℝ-bundles
Abstract
The reduction of mechanical presymplectic structures and its application to the reduction of time-dependent Hamiltonian systems were developed in a recent paper (Gutiérrez Sagredo et al, 2025). This approach overcomes some limitations of the original Albert reduction (Albert, 1989). In this paper we will describe the reduction of time-dependent Hamiltonian systems using the extended formalism. This process combines cotangent bundle reduction with reduction of presymplectic structures of corank 1 and 2. These results generalize previous work (Lacirasella et al, 2012), in the same direction. Several examples will be presented to illustrate the theory from this new perspective.
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BibTeX
@misc{benitez2026reduction,
title = {{Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal $\mathbbR$-bundles}},
author = {C. Benítez and D. Iglesias Ponte and J. C. Marrero and E. Padrón},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28278},
eprint = {2608.28278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28278},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal ℝ-bundles
AU - C. Benítez
AU - D. Iglesias Ponte
AU - J. C. Marrero
AU - E. Padrón
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.28278
UR - https://arxiv.org/abs/2608.28278
AB - The reduction of mechanical presymplectic structures and its application to the reduction of time-dependent Hamiltonian systems were developed in a recent paper (Gutiérrez Sagredo et al, 2025). This approach overcomes some limitations of the original Albert reduction (Albert, 1989). In this paper we will describe the reduction of time-dependent Hamiltonian systems using the extended formalism. This process combines cotangent bundle reduction with reduction of presymplectic structures of corank 1 and 2. These results generalize previous work (Lacirasella et al, 2012), in the same direction. Several examples will be presented to illustrate the theory from this new perspective.
ER -