On the -stability conjecture
Jacob Palis (1987)
Publications Mathématiques de l'IHÉS
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Jacob Palis (1987)
Publications Mathématiques de l'IHÉS
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Feliks Przytycki (1977)
Studia Mathematica
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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.
J. Delgado, N. Romero, A. Rovella, F. Vilamajó (2007)
Fundamenta Mathematicae
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Sufficient conditions for a map having nonwandering critical points to be Ω-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of Ω-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom A maps that have no cycles but are not Ω-stable.
J. Iglesias, A. Portela, A. Rovella (2010)
Fundamenta Mathematicae
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We give here the first examples of C¹ structurally stable maps on manifolds of dimension greater than two that are neither diffeomorphisms nor expanding. It is shown that an Axiom A endomorphism all of whose basic pieces are expanding or attracting is C¹ stable. A necessary condition for the existence of such examples is also given.
Carvalho, Maria (1996)
Portugaliae Mathematica
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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.
Janina Kotus, Fopke Klok (1988)
Compositio Mathematica
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S. Smale (1963)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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