Stability and genericity in dynamical systems
Stephen Smale (1969-1970)
Séminaire Bourbaki
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Stephen Smale (1969-1970)
Séminaire Bourbaki
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S. Smale (1963)
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Roger C. McCann (1972)
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Absolute stability of a compact set is characterized by the cardinality of a fundamental system of positively invariant neighborhoods.
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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.