Quadratic Morse-Smale Vector Fields which are not Structurally Stable

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 May 1982Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 85, page 125 (issn: 0002-9939,

Copyright policy )

Authors: Chicone, Carmen; Shafer, Douglas S.;

doi: 10.2307/2043296 , 10.1090/s0002-9939-1982-0647911-9

Quadratic Morse-Smale Vector Fields which are not Structurally Stable

- Summary
- Subjects
- Metrics

Abstract

An example is given of a quadratic system in the plane which is Morse-Smale but not structurally stable. Also, it is proved that no such example exists for a quadratic system which is a gradient.

Keywords

Morse-Smale systems, quadric system in the plane, Cr-Whitney topology, quadratic gradient Morse-Smale systems, Stability theory for smooth dynamical systems, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Structural stability and analogous concepts of solutions to ordinary differential equations, Local and nonlocal bifurcation theory for dynamical systems, nonwandering set

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	1
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average