The index of stable critical points

DOI10.1016/S0166-8641(02)00087-1zbMath1013.37016OpenAlexW1986627117MaRDI QIDQ1867184

Christian Bonatti, Jordi Villadelprat

Publication date: 2 April 2003

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0166-8641(02)00087-1

zbMATH Keywords

stabilityvector fieldplug constructionisolated critical point

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Degree, winding number (55M25) Stability of solutions to ordinary differential equations (34D20) Dynamics induced by flows and semiflows (37C10) Critical points and critical submanifolds in differential topology (57R70)

Related Items (4)

Planar isolated and stable fixed points have index =1 ⋮ Translation Arcs and Stability in Two Dimensions ⋮ Indices of the iterates of \(\mathbb R^3\)-homeomorphisms at Lyapunov stable fixed points ⋮ Realization of all Dold's congruences with stability

Cites Work

• Der Abbildungsgrad von Vektorfeldern zu stabilen Ruhelagen. (The topological degree of vector fields of stable equilibrium)
• Deformation of a system into an asymptotically stable system
• Instability of equilibria in dimension three
• A Poincaré-Hopf theorem for noncompact manifolds
• Stable equilibria and vector field index
• On the minimal sets of non-singular vector fields
• On a topological obstruction to regular forms of stability
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