On Ω-stability of flows

Malta, Iaci

doi:10.1007/bf02584876

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The Set Consisting Of Morse-smale Fields Is Open and Nonempt1

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1982

1992

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“…Later Newhouse [69] showed that it is enough for a-stability to require the hyperbolicity and nonexistence of cycles on the limit set. More recently, Malta [50], [51] weakened this hypothesis to the Birkhoff centre, which is defined as the closure of those orbits that are simultaneously ex-and a)-recurrent. In the opposite direction, it is known that if I satisfies Axiom A and there exist cycles in O(f) then I is not a-stable [76].…”

Section: The Set Consisting Of Morse-smale Fields Is Open and Nonemptmentioning

confidence: 99%