Perturbing a product of stable flows
Manning, Anthony. (2005) Perturbing a product of stable flows. Proceedings of the American Mathematical Society, Vol.133 (No.6). pp. 1693-1697. ISSN 0002-9939Full text not available from this repository.
Official URL: http://www.jstor.org/stable/4097706
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|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Proceedings of the American Mathematical Society|
|Publisher:||American Mathematical Society|
|Number of Pages:||5|
|Page Range:||pp. 1693-1697|
|Access rights to Published version:||Restricted or Subscription Access|
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