On differential equations in normal form

DOI10.1007/BF01445209zbMath0754.34032MaRDI QIDQ1191429

Sebastian Walcher

Publication date: 27 September 1992

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164868

zbMATH Keywords

reductionnormal formsnon-elementary stationary points

Mathematics Subject Classification ID

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

Related Items (33)

Lie algebras with finite-dimensional polynomial centralizer ⋮ POINCARÉ NORMAL FORMS AND SIMPLE COMPACT LIE GROUPS ⋮ Symmetry of stochastic non-variational differential equations ⋮ Automorphisms and derivations of differential equations and algebras ⋮ Local Darboux first integrals of analytic differential systems ⋮ RESONANT NORMAL FORMS AS CONSTRAINED LINEAR SYSTEMS ⋮ Orbit space reduction and localizations ⋮ Centralizers of locally nilpotent derivations ⋮ Non-quadratic additional conserved quantities in Birkhoff normal forms ⋮ Centralizers and normalizers of local analytic and formal vector fields ⋮ Invariant ideals of local analytic and formal vector fields ⋮ Tikhonov-Fenichel reduction for parameterized critical manifolds with applications to chemical reaction networks ⋮ First integrals of local analytic differential systems ⋮ Properties of monodromic points on center manifolds in \(\mathbb R^3\) via Lie symmetries ⋮ Resonant bifurcations ⋮ Isochronous dynamical systems ⋮ Conjugacy of vector fields respecting additional properties. ⋮ On convergent normal from transformations in presence of symmetries ⋮ Lowering the dimension of polynomial vector fields in R2 and R3 ⋮ Invariant manifolds of an autonomous ordinary differential equation from its generalized normal forms ⋮ Local integrability of Poincaré-Dulac normal forms ⋮ Reduction and reconstruction for symmetric ordinary differential equations ⋮ Normal forms of maps: Formal and algebraic aspects ⋮ Painlevé analysis and normal forms theory ⋮ Embedding and splitting ordinary differential equations in normal form ⋮ Two New Classes of Isochronous Hamiltonian Systems ⋮ Singular complete integrability ⋮ Analytical approach for simplifying dynamical systems of polynomial type. ⋮ Complete integrability of diffeomorphisms and their local normal forms ⋮ Equivariant N-Dof Hamiltonians Via Generalized Normal Forms ⋮ PERIODIC ORBITS OF THE LORENZ SYSTEM THROUGH PERTURBATION THEORY ⋮ On the Poincaré problem ⋮ Generalized normal forms for polynomial vector fields

Cites Work

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• Reduction of the semisimple \(1:1\) resonance
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The Hamiltonian Hopf bifurcation
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Über die Invarianten von linearen Gruppen
• Singularities of vector fields
• Normal form and representation theory

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