Skip to content
DraconiticResearch
Search Sources API
185,139 studies31 sourcesUpdated 35 min ago
PreprintCC BY 4.0HAL

Butcher series for Hamiltonian Poisson integrators through symplectic groupoids

  • Adrien Busnot Laurent
  • Oscar Cosserat
Open at sourcePDFCite

Abstract

We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, use Butcher trees to compute the Taylor series of a solution of a Hamilton-Jacobi equation on any symplectic groupoid 𝒒 rightrightarrows M. The impact of this new algebraic approach is twofold. On the geometric side, it yields algebraic operations to approximate Lagrangian bisections of 𝒒 using the Butcher-Connes-Kreimer Hopf algebra and, in turn, aims at a better understanding of the group of Hamiltonian diffeomorphisms of M. On the computational side, we define a new class of Poisson integrators for Hamiltonian dynamics on Poisson manifolds.

Related

  1. Symplectic groupoid multiplication and Poisson integrators
    Alejandro Cabrera, David Iglesias Ponte, Juan Carlos Marrero
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. The shifted symplectic geometry of derived higher groupoids
    Miquel Cueca, Florian Dorsch, Reyer Sjamaar +1
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  3. Moment Lagrangians, unobstructedness and symplectic groupoids
    Yan-Lung Leon Li
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Dynamics of Stochastic Hamiltonian systems I - Wong-Zakai Variational integrators
    Jacky Cresson, Rouba SAfI
    HALPreprintCC BY-NC-ND 4.0Full textDynamical systemsNumerical analysis & scientific computingHALarXiv
  5. The symplectic leaves of the affine Poisson C∞-scheme associated with a singular subalgebroid
    Ruben Louis
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{laurent2026butcher,
  title = {{Butcher series for Hamiltonian Poisson integrators through symplectic groupoids}},
  author = {Adrien Busnot Laurent and Oscar Cosserat},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05368917v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Butcher series for Hamiltonian Poisson integrators through symplectic groupoids
AU  - Adrien Busnot Laurent
AU  - Oscar Cosserat
PY  - 2026
DA  - 2026/10/09
PB  - HAL
UR  - https://hal.science/hal-05368917v2
AB  - We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, use Butcher trees to compute the Taylor series of a solution of a Hamilton-Jacobi equation on any symplectic groupoid 𝒒 rightrightarrows M. The impact of this new algebraic approach is twofold. On the geometric side, it yields algebraic operations to approximate Lagrangian bisections of 𝒒 using the Butcher-Connes-Kreimer Hopf algebra and, in turn, aims at a better understanding of the group of Hamiltonian diffeomorphisms of M. On the computational side, we define a new class of Poisson integrators for Hamiltonian dynamics on Poisson manifolds.
ER  -