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Symplectic Geometric Algorithms for Hamiltonian Systems

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Cover of 'Symplectic Geometric Algorithms for Hamiltonian Systems'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Preliminaries of Differentiable Manifolds
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    Chapter 3 Symplectic Algebra and Geometry Preliminaries
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    Chapter 4 Hamiltonian Mechanics and Symplectic Geometry
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    Chapter 5 Symplectic Difference Schemes for Hamiltonian Systems
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    Chapter 6 The Generating Function Method
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    Chapter 7 The Calculus of Generating Functions and Formal Energy
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    Chapter 8 Symplectic Runge-Kutta Methods
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    Chapter 9 Composition Scheme
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    Chapter 10 Formal Power Series and B-Series
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    Chapter 11 Volume-Preserving Methods for Source-Free Systems
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    Chapter 12 Contact Algorithms for Contact Dynamical Systems
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    Chapter 13 Poisson Bracket and Lie-Poisson Schemes
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    Chapter 14 KAM Theorem of Symplectic Algorithms
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    Chapter 15 Lee-Variational Integrator
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    Chapter 16 Structure Preserving Schemes for Birkhoff Systems
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    Chapter 17 Multisymplectic and Variational Integrators
Attention for Chapter 4: Hamiltonian Mechanics and Symplectic Geometry
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