Hamilton Poisson İntegratörleri İçin Semplektik Gruployitler Aracılığıyla Butcher Serileri

Özet (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.

Yazarların özeti; kaynağından alınmıştır. Annali di Matematica Pura ed Applicata (1923 -), 2026 · DOI ↗