On the structure of nilpotent normal form modules

DOI10.1006/jdeq.2001.4058zbMath1012.34036OpenAlexW1998751687MaRDI QIDQ1614724

James A. Murdock

Publication date: 8 September 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4058

zbMATH Keywords

normal formsStanley decompositionequivariants

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items (12)

A new transvectant algorithm for nilpotent normal forms ⋮ Stanley depth and the lcm-lattice ⋮ Box products in nilpotent normal form theory: the factoring method ⋮ Stanley decomposition of the joint covariants of three quadratics ⋮ Normal form for high-dimensional nonlinear system and its application to a viscoelastic moving belt ⋮ Block Stanley decompositions. II: Greedy algorithms, applications, and open problems ⋮ Vector potential normal form classification for completely integrable solenoidal nilpotent singularities ⋮ On the representations and \(\mathbb{Z}_2\)-equivariant normal form for solenoidal Hopf-zero singularities ⋮ Block Stanley decompositions. I: Elementary and gnomon decompositions ⋮ Normal Forms for Coupled Takens-Bogdanov Systems ⋮ How to compute the Stanley depth of a module ⋮ An improved theory of asymptotic unfoldings

Cites Work

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• A simple global characterization for normal forms of singular vector fields
• Normal form for the (2;n)-nilpotent vector field, using invariant theory
• Computing combinatorial decompositions of rings
• Asymptotic unfoldings of dynamical systems by normalizing beyond the normal form
• EQUIVALENCE AND NORMAL FORMS OF GERMS OF SMOOTH MAPPINGS
• Algorithms in invariant theory

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