The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators
DOI10.3934/jcd.2023011arXiv2307.07984OpenAlexW4389197457MaRDI QIDQ6201385
Publication date: 20 February 2024
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2307.07984
Noether's theoremgeometric numerical integrationEuler-Lagrange complexvolume-preservationaromatic bicomplexaromatic Lie derivativesolenoidal forms
Trees (05C05) Variational principles in infinite-dimensional spaces (58E30) de Rham theory in global analysis (58A12) Differential complexes (58J10) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Algebraic geometry (14-XX)
Cites Work
- Two interacting Hopf algebras of trees: a Hopf-algebraic approach to composition and substitution of B-series.
- B-series methods are exactly the affine equivariant methods
- On a pre-Lie algebra defined by insertion of rooted trees
- B-series methods cannot be volume-preserving
- On the Butcher group and general multi-value methods
- Hopf algebras, renormalization and noncommutative geometry
- Volume-preserving algorithms for source-free dynamical systems
- Algebraic structures of B-series
- Backward error analysis for multistep methods
- The universal pre-Lie-Rinehart algebras of aromatic trees
- Constructing general rough differential equations through flow approximations
- Detecting and determining preserved measures and integrals of birational maps
- Algebraic structure of aromatic B-series
- Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
- Discretization of the Lagrange Top
- Discretization of the Euler Top
- Long Time Accuracy of Lie--Trotter Splitting Methods for Langevin Dynamics
- Lois Pré-Lie En Interaction
- Preserving first integrals and volume forms of additively split systems
- On the Lie enveloping algebra of a pre-Lie algebra
- Invariant variation problems
- An operadic approach to substitution in Lie–Butcher series
- Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs
- An Algebraic Theory of Integration Methods
- Aromatic Butcher series
- The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators
