Lowering the dimension of polynomial vector fields in R2 and R3

DOI10.1063/1.1355662zbMath1080.34529OpenAlexW1633696936WikidataQ73463032 ScholiaQ73463032MaRDI QIDQ5706255

Patricia Yanguas

Publication date: 7 November 2005

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1355662

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Normal forms for dynamical systems (37G05) Dynamics induced by flows and semiflows (37C10)

Related Items (5)

Non-quadratic additional conserved quantities in Birkhoff normal forms ⋮ Dissipative-Hamiltonian decomposition of smooth vector fields based on symmetries ⋮ Elie Cartan and pan-geometry of multispatial hyperspace ⋮ Invariant manifolds of an autonomous ordinary differential equation from its generalized normal forms ⋮ PERIODIC ORBITS OF THE LORENZ SYSTEM THROUGH PERTURBATION THEORY

Cites Work

• A simple global characterization for normal forms of singular vector fields
• On differential equations in normal form
• A splitting lemma for equivariant dynamics
• On convergent normal from transformations in presence of symmetries
• Reduction of Polynomial Planar Hamiltonians with Quadratic Unperturbed Part
• Reduction of polynomial Hamiltonians by the construction of formal integrals
• Expansion formulae in canonical transformations depending on a small parameter
• On a perturbation theory using Lie transforms

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