Stability and genericity in dynamical systems
Stephen Smale (1969-1970)
Séminaire Bourbaki
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Displaying similar documents to “On the -stability conjecture”
Stability and genericity in dynamical systems
Correction to: Connecting invariant manifolds and the solution of the stability and -stability conjectures for flows.
Hayashi, Shuhei (1999)
Annals of Mathematics. Second Series
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On Ω-stability and structural stability of endomorphisms satisfying Axiom A
Feliks Przytycki (1977)
Studia Mathematica
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Ω-stability for maps with nonwandering critical points
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.
C¹-maps having hyperbolic periodic points
N. Aoki, Kazumine Moriyasu, N. Sumi (2001)
Fundamenta Mathematicae
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We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.
Abundance of hyperbolicity in the topology
Raúl Ures (1995)
Annales scientifiques de l'École Normale Supérieure
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A global perspective for non-conservative dynamics
J. Palis (2005)
Annales de l'I.H.P. Analyse non linéaire
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Bifurcations and stability of families of diffeomorphisms
Sheldon E. Newhouse, Jacob Palis, Floris Takens (1983)
Publications Mathématiques de l'IHÉS
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The interior of zero entropy diffeomorphisms.
Carvalho, Maria (1996)
Portugaliae Mathematica
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A sufficient condition for -stability of vector fields on open manifolds
Janina Kotus, Fopke Klok (1988)
Compositio Mathematica
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C¹ stable maps: examples without saddles
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.