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Perturbing a product of stable flows
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Manning, Anthony (2005) Perturbing a product of stable flows. Proceedings of the American Mathematical Society, Vol.133 (No.6). pp. 1693-1697. doi:10.1090/S0002-9939-05-07872-X ISSN 0002-9939.
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Official URL: http://www.jstor.org/stable/4097706
Abstract
Suppose that f and f' are axiom A flows with attractors A and A'. Then the attractor A x A' for the product flow g(t) = f(t) x f(t)' on the product manifold is no longer hyperbolic ( although there is a hyperbolic action of R-2).
It is easy to see that the attractor cannot explode but we show here that it cannot implode: for any flow (h(t)) sufficiently close to (g(t)) any attractor whose basin is not too thin is epsilon-dense in A x A'.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9939 | ||||
Official Date: | 2005 | ||||
Dates: |
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Volume: | Vol.133 | ||||
Number: | No.6 | ||||
Number of Pages: | 5 | ||||
Page Range: | pp. 1693-1697 | ||||
DOI: | 10.1090/S0002-9939-05-07872-X | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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