Stable topological transitivity properties of ℝn-extensions of hyperbolic transformations
2011 ◽
Vol 32
(4)
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pp. 1435-1443
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Keyword(s):
Axiom A
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AbstractWe consider ℝn skew-products of a class of hyperbolic dynamical systems. It was proved by Niţică and Pollicott [Transitivity of Euclidean extensions of Anosov diffeomorphisms. Ergod. Th. & Dynam. Sys. 25 (2005), 257–269] that for an Anosov diffeomorphism ϕ of an infranilmanifold Λ there is (subject to avoiding natural obstructions) an open and dense set f:Λ→ℝN for which the skew-product ϕf(x,v)=(ϕ(x),v+f(x)) on Λ×ℝN has a dense orbit. We prove a similar result in the context of an Axiom A hyperbolic flow on an attractor.
2014 ◽
Vol 35
(6)
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pp. 1814-1845
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1998 ◽
Vol 18
(2)
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pp. 471-486
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2009 ◽
Vol 30
(2)
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pp. 361-377
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Keyword(s):
2019 ◽
Vol 373
(1)
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pp. 629-664
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Keyword(s):