Asymptotic unfoldings of dynamical systems by normalizing beyond the normal form

DOI10.1006/jdeq.1997.3368zbMath0898.34038OpenAlexW2003479622MaRDI QIDQ1381631

James A. Murdock

Publication date: 2 November 1998

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

Full work available at URL: https://semanticscholar.org/paper/305549f0ac561d5c8bf6727e47152e4149476b74

zbMATH Keywords

normal form theoryperturbed dynamical systemuniversal unfoldingsasymptotic unfoldingArnold's unfoldingnormalizing beyond the normal formsimplification of the normal formspecial normal form

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Normal forms for dynamical systems (37G05)

Related Items (8)

On the structure of nilpotent normal form modules ⋮ Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory ⋮ The k-Zero Bifurcation Theorem for m-Parameterized Systems ⋮ Box products in nilpotent normal form theory: the factoring method ⋮ Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case ⋮ Bifurcation Control and Universal Unfolding for Hopf-Zero Singularities with Leading Solenoidal Terms ⋮ FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS ⋮ An improved theory of asymptotic unfoldings

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A simple global characterization for normal forms of singular vector fields
• Hopf bifurcation with non-semisimple 1:1 resonance
• Bifurcations associated with a three-fold zero eigenvalue
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