Equivariant decomposition of polynomial vector fields

DOI10.1142/S0219199720500832zbMath1498.17040arXiv1909.06955OpenAlexW3092239033MaRDI QIDQ5016195

Jan A. Sanders, Fahimeh Mokhtari

Publication date: 13 December 2021

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.06955

zbMATH Keywords

invariant theoryClebsch-Gordan coefficientsEuler vector fieldnilpotent singularityunique normal forminversion of the Clebsch-Gordan coefficients

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Lie algebras of vector fields and related (super) algebras (17B66) Vector and tensor algebra, theory of invariants (15A72) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Normal forms for nonlinear problems in mechanics (70K45)

Cites Work

• Holomorphic normal form of nonlinear perturbations of nilpotent vector fields
• Unique normal forms: The nilpotent Hamiltonian case
• Further reduction of the Takens-Bogdanov normal form
• Normal form theory and spectral sequences.
• Vector potential normal form classification for completely integrable solenoidal nilpotent singularities
• Versal normal form for nonsemisimple singularities
• A NOTE ON THE TRIPLE-ZERO LINEAR DEGENERACY: NORMAL FORMS, DYNAMICAL AND BIFURCATION BEHAVIORS OF AN UNFOLDING
• A rational theory of Clebsch-Gordan coefficients
• Averaging methods in nonlinear dynamical systems
• Lie groups beyond an introduction
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