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The aromatic bicomplex is an algebraic tool based on aromatic Butcher treesand used in particular for the explicit description of volume-preservingaffine-equivariant numerical integrators. The present work defines new toolsinspired from variational calculus such as the Lie derivative, differentconcepts of symmetries, and Noether's theory in the context of aromaticforests. The approach allows to draw a correspondence between aromaticvolume-preserving methods and symmetries on the Euler-Lagrange complex, towrite Noether's theorem in the aromatic context, and to describe the aromaticB-series of volume-preserving methods explicitly with the Lie derivative.

The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators