Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Perturbing a product of stable flows

Author(s): Anthony Manning
Journal: Proc. Amer. Math. Soc. 133 (2005), 1693-1697.
MSC (2000): Primary 37C70, 37C75, 37D20; Secondary 37D10, 37C27
Posted: January 13, 2005
MathSciNet review: 2120252
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Abstract | References | Similar articles | Additional information

Abstract: Suppose that and are axiom A flows with attractors and . Then the attractor $A \times A'$ for the product flow $g_t =f_t \times f'_t$ on the product manifold is no longer hyperbolic (although there is a hyperbolic action of $\mathbb{R}^2$ ).

It is easy to see that the attractor cannot explode but we show here that it cannot implode: for any flow sufficiently close to any attractor whose basin is not too thin is $\varepsilon$ -dense in $A \times A'$ .

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