Structural stability and generic properties of planar polynomial vector fields.
Douglas S. Shafer (1987)
Revista Matemática Iberoamericana
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Douglas S. Shafer (1987)
Revista Matemática Iberoamericana
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J. Auslander, P. Seibert (1964)
Annales de l'institut Fourier
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Les auteurs étudient la notion de prolongement au sens de T. Ura et ses relations avec la notion d’ensembles positivement invariants. La stabilité au sens de Liapounoff est équivalente à l’invariance par prolongement. Les auteurs dégagent ensuite la notion de “prolongements abstraits” et les notions de stabilité correspondantes; la stabilité absolue (associée au prolongement minimal transitif) et la stabilité asymptotique jouent un rôle important.
Marco Antonio Teixeira (1997)
Publicacions Matemàtiques
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In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
Sheldon E. Newhouse, Jacob Palis, Floris Takens (1983)
Publications Mathématiques de l'IHÉS
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S. Sergio Plaza (1994)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Roger C. McCann (1972)
Annales de l'institut Fourier
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Absolute stability of a compact set is characterized by the cardinality of a fundamental system of positively invariant neighborhoods.
J. Iglesias, A. Portela, A. Rovella (2009)
Fundamenta Mathematicae
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A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of C¹ endomorphisms with singularities. A map that is stable in this sense is conjugate to each perturbation that is equivalent to it in a geometric sense. It is shown that this kind of stability implies Axiom A and Ω-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of C³ structurally stable maps.
Hayashi, Shuhei (1998)
Documenta Mathematica
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Lupu, Mircea, Florea, Olivia, Lupu, Ciprian (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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