Generating functions and volume preserving mappings

DOI10.3934/dcds.2014.34.1229zbMath1278.53085OpenAlexW2053421210MaRDI QIDQ379803

Huiyan Xue, Antonella Zanna

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.1229

zbMATH Keywords

differential formsgenerating functionsymplecticvolume preservation

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Canonical transformations in symplectic and contact geometry (53D22) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (2)

A classification of volume preserving generating forms in \(\mathbb{R}^3\) ⋮ Locally-symplectic neural networks for learning volume-preserving dynamics

Cites Work

• Generating forms for exact volume-preserving maps
• A representation theorem for volume-preserving transformations
• B-series methods cannot be volume-preserving
• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• Volume-preserving algorithms for source-free dynamical systems
• Explicit volume-preserving splitting methods for polynomial divergence-free vector fields
• The invariance of Poincaré's generating function for canonical transformations
• The method of orthogonal projection in potential theory
• Splitting methods
• Discrete mechanics and variational integrators
• Preserving first integrals and volume forms of additively split systems
• Volume-preserving maps, source-free systems and their local structures
• Geometric Numerical Integration
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