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Discrete Mechanics, Geometric Integration and Lie–Butcher Series

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Cover of 'Discrete Mechanics, Geometric Integration and Lie–Butcher Series'

Table of Contents

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    Book Overview
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    Chapter 1 Why Geometric Numerical Integration?
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    Chapter 2 Lie Group Integrators
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    Chapter 3 Lie–Butcher Series, Geometry, Algebra and Computation
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    Chapter 4 Averaging and Computing Normal Forms with Word Series Algorithms
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    Chapter 5 Combinatorial Hopf Algebras for Interconnected Nonlinear Input-Output Systems with a View Towards Discretization
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    Chapter 6 Computational Aspects of Some Exponential Identities
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    Chapter 7 Post-Lie Algebras, Factorization Theorems and Isospectral Flows
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    Chapter 8 Overview of (pro-)Lie Group Structures on Hopf Algebra Character Groups
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    Chapter 9 Bäcklund Transformations in Discrete Variational Principles for Lie-Poisson Equations
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    Chapter 10 Numerical Precession in Variational Discretizations of the Kepler Problem
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    Chapter 11 Full Affine Equivariance and Weak Natural Transformations in Numerical Analysis—The Case of B-Series
Attention for Chapter 9: Bäcklund Transformations in Discrete Variational Principles for Lie-Poisson Equations
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