Annali di Matematica Pura ed Applicata (1923 -)· 2026Q1
Butcher series for Hamiltonian Poisson integrators through symplectic groupoids
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- 2026year
Short summary
A new pre-Lie algebra and Butcher trees are used to compute Taylor series for Hamilton-Jacobi equations on symplectic groupoids, leading to novel Poisson integrators for Hamiltonian dynamics.
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Key points
- Introduces a new pre-Lie algebra in the context of symplectic groupoids.
- Applies Butcher trees to compute Taylor series for Hamilton-Jacobi equations on symplectic groupoids.
- Develops algebraic operations for approximating Lagrangian bisections.
- Defines a new class of Poisson integrators for Hamiltonian dynamics on Poisson manifolds.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 $$\mathcal {G} \rightrightarrows M.$$ The impact of this new algebraic approach is twofold. On the geometric side, it yields algebraic operations to approximate Lagrangian bisections of $$\mathcal {G} $$ 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.
The authors' abstract, as published at the source. Annali di Matematica Pura ed Applicata (1923 -), 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics