Hypernormal forms for equilibria of vector fields. Codimension one linear degeneracies

DOI10.1216/rmjm/1181071677zbMath0930.34027OpenAlexW2077502387MaRDI QIDQ1293279

Estanislao Gamero, Antonio Algaba, Emilio Freire

Publication date: 31 January 2000

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL29-1/CONT29-1/CONT29-1.html

zbMATH Keywords

normal form theoryHopf singularitysaddle-node singularitycodimension one linear degeneracieshypernormal formsPoincaré-Dulac-Birkhoff theorem

Mathematics Subject Classification ID

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

Related Items (13)

Analytic integrability inside a family of degenerate centers ⋮ Computing simplest normal forms for the Takens-Bogdanov singularity ⋮ Unique normal form of a class of 3 dimensional vector fields with symmetries ⋮ Simplest Normal Forms of Hopf–Neimark–Sacker Bifurcations ⋮ Hypernormal form theory: foundations and algorithms ⋮ Reversibility and quasi-homogeneous normal forms of vector fields ⋮ Isochronicity via normal form ⋮ Characterizing orbital-reversibility through normal forms ⋮ Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system ⋮ Characterizing isochronous points and computing isochronous sections ⋮ An improved theory of asymptotic unfoldings ⋮ Quasi-homogeneous normal forms ⋮ Computation of the simplest normal forms with perturbation parameters based on Lie transform and rescaling

Cites Work

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• Normal forms for nonlinear vector fields. II. Applications
• Normal forms for singularities of vector fields
• Normal forms for nonlinear vector fields. I. Theory and algorithm
• Hypernormal Form for the Hopf-Zero Bifurcation
• Canonical transformations depending on a small parameter

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