Singularities of vector fields on ℝ3 determined by their first non-vanishing jet

DOI10.1017/S0143385700004971zbMath0661.58005OpenAlexW2003307944MaRDI QIDQ3810558

Freddy Dumortier, Sebastian J. van Strien, Patrick Bonckaert

Publication date: 1989

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700004971

zbMATH Keywords

vector fieldsingularityhomogeneous vector field

Mathematics Subject Classification ID

Jets in global analysis (58A20) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items (11)

Infinitesimal Hartman-Grobman Theorem in Dimension Three ⋮ Stability of vector fields on \({\mathbb{R}}^ 3\) determined by the first non- vanishing jet ⋮ Differentiability of the conjugacy in the Hartman-Grobman Theorem ⋮ Topological equivalence for saddle connections ⋮ Transition functions and moduli of stability for 3-dimensional homogeneous vector fields with a hyperbolic blowing-up ⋮ Periodic solutions of homogeneous equations ⋮ Genericity of hyperbolic homogeneous vector fields in \(\mathbb{R}^ 3\) ⋮ Topological equivalence for chains of saddle-connections ⋮ Conjugacy of normally tangent diffeomorphisms: A tool for treating moduli of stability ⋮ On the local structure of real vector fields at a dicritical singularity ⋮ Smooth linearization of hyperbolic fixed points without resonance conditions

Cites Work

• Unnamed Item
• A contribution to the topological classification of homogeneous vector fields in \(R^ 3\)
• Normal hyperbolicity and linearisability
• Moduli of stability for germs of homogeneous vectorfields on \(R^ 3\)
• Singularities of gradient vector-fields in \(R^ 3\).
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Geometric Properties of Homogeneous Vector Fields of Degree Two in R 3
• On a Theorem of P. Hartman

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