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Discrete Mechanics, Geometric Integration and Lie–Butcher Series [2018]

1
Why Geometric Numerical Integration?
29
Lie Group Integrators
71
Lie–Butcher Series, Geometry, Algebra and Computation
115
Averaging and Computing Normal Forms with Word Series Algorithms
139
Combinatorial Hopf Algebras for Interconnected Nonlinear Input-Output Systems with a View Towards Discretization
185
Computational Aspects of Some Exponential Identities
231
Post-Lie Algebras, Factorization Theorems and Isospectral Flows
287
Overview of (pro-)Lie Group Structures on Hopf Algebra Character Groups
315
Bäcklund Transformations in Discrete Variational Principles for Lie-Poisson Equations
333
Numerical Precession in Variational Discretizations of the Kepler Problem
349
Full Affine Equivariance and Weak Natural Transformations in Numerical Analysis—The Case of B-Series
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