The Lie derivative and Noether's theorem on the aromatic bicomplex

07/16/2023

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by   Adrien Laurent, et al.

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The aromatic bicomplex is an algebraic tool based on aromatic Butcher-trees and used in particular for the explicit description of volume-preserving affine-equivariant numerical integrators. To further understand the links between geometric numerical integration and variational calculus, as well as to describe more precisely the form of volume-preserving methods, we define and study the Lie derivative and the concept of symmetries on the aromatic bicomplex. We give an aromatic formulation of Noether's theorem and adapt the approach in the context of numerical volume-preservation.