Embedding and splitting ordinary differential equations in normal form

DOI10.1016/j.jde.2005.06.025zbMath1091.37017OpenAlexW2032244785MaRDI QIDQ2493093

Giuseppe Gaeta, Sebastian Walcher

Publication date: 9 June 2006

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

Full work available at URL: https://doi.org/10.1016/j.jde.2005.06.025

zbMATH Keywords

reduced systemembeddingperturbationsnormal formssymmetric systemsanalytic vector fieldnonautonomous linear systems

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of ordinary differential equations (34D10) Normal forms for dynamical systems (37G05) Dynamics induced by flows and semiflows (37C10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Topological dynamics of nonautonomous systems (37B55)

Related Items (4)

Symmetry of stochastic non-variational differential equations ⋮ On the geometry of twisted prolongations, and dynamical systems ⋮ Poincaré-like approach to Landau theory. I. General theory ⋮ Reduction and reconstruction for symmetric ordinary differential equations

Cites Work

• Reducible ordinary differential equations
• The Hamiltonian Hopf bifurcation
• A simple global characterization for normal forms of singular vector fields
• On differential equations in normal form
• Finitely differentiable invariants
• Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts
• Normal form theory and spectral sequences.
• \(C^\infty\)-normal forms of local vector fields
• Convergence of normal form transformations: The Role of symmetries
• Bifurcations in Hamiltonian systems. Computing singularities by Gröbner bases
• A splitting lemma for equivariant dynamics
• Bifurcations of Relative Equilibria
• Normal Forms and Unfoldings for Local Dynamical Systems
• RESONANT NORMAL FORMS AS CONSTRAINED LINEAR SYSTEMS
• Dimension Increase and Splitting for Poincaré-Dulac Normal Forms
• Quaternionic-like bifurcation in the absence of symmetry
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