Quadratic gradients on the plane are generically Morse-Smale

DOI10.1016/0022-0396(79)90085-8zbMath0378.34041OpenAlexW2076556665MaRDI QIDQ1246826

Carmen C. Chicone

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0022-0396(79)90085-8

Mathematics Subject Classification ID

Stability theory for ordinary differential equations (34D99)

Related Items

Constant unfoldings of saddle connections in planar flows, Quadratic Morse-Smale Vector Fields which are not Structurally Stable, The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity, Gradient systems of harmonic polynomials, The Riemann problem for 2\(\times 2\) systems of hyperbolic conservation laws with case I quadratic nonlinearities, Dependence on the Background Viscosity of Solutions to a Prototypical NonStrictly Hyperbolic System of Conservation Laws, Bifurcation under parameter change of Riemann solutions for nonstrictly hyperbolic systems, Planar quadratic vector fields with finite saddle connection on a straight line (convex case), Multiple Viscous Solutions for Systems of Conservation Laws, Phase portraits of the quadratic polynomial Liénard differential systems, Stabilité locale des systèmes quadratiques, Bifurcations in gradient dynamical systems, VISCOUS SHOCK PROFILES FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH AN UMBILIC POINT, Riemann problems requiring a viscous profile entropy condition

Cites Work

• Structural stability on two-dimensional manifolds
• On gradient dynamical systems
• A survey of quadratic systems
• Structurally stable systems on open manifolds are never dense
• On Morse-Smale dynamical systems
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