PreprintCC BY 4.0arXiv
Symplectic groupoid multiplication and Poisson integrators
Abstract
In this paper, we study the role of local symplectic groupoid multiplication in the construction of approximation methods for Hamiltonian flows on the underlying Poisson manifold. We show it can be used to construct a novel multiplicative type of approximating sequences for the relevant Lagrangian bisection. We describe the corresponding theoretical results, their practical implementation into approximation methods on coordinate charts via generating functions, and illustrative examples.
Related
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- The symplectic leaves of the affine Poisson C∞-scheme associated with a singular subalgebroid
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- A characterization of simplicity of reduced groupoid C*-algebras
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BibTeX
@misc{cabrera2026symplectic,
title = {{Symplectic groupoid multiplication and Poisson integrators}},
author = {Alejandro Cabrera and David Iglesias Ponte and Juan Carlos Marrero},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20911},
eprint = {2610.20911},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20911},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symplectic groupoid multiplication and Poisson integrators
AU - Alejandro Cabrera
AU - David Iglesias Ponte
AU - Juan Carlos Marrero
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20911
UR - https://arxiv.org/abs/2610.20911
AB - In this paper, we study the role of local symplectic groupoid multiplication in the construction of approximation methods for Hamiltonian flows on the underlying Poisson manifold. We show it can be used to construct a novel multiplicative type of approximating sequences for the relevant Lagrangian bisection. We describe the corresponding theoretical results, their practical implementation into approximation methods on coordinate charts via generating functions, and illustrative examples.
ER -