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arXiv · 2608.28278

Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal $\mathbb{R}$-bundles

C. Benítez·D. Iglesias Ponte·J. C. Marrero·E. Padrón
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Abstract

The reduction of mechanical presymplectic structures and its application to the reduction of time-dependent Hamiltonian systems were developed in a recent paper (Guti\'errez 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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C. Benítez, D. Iglesias Ponte, J. C. Marrero, E. Padrón. 2026-08-28. Reduction of symmetric time-dependent Hamiltonian systems I: presymplectic principal $\mathbb{R}$-bundles. https://arxiv.org/abs/2608.28278

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