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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Perturbing a product of stable flows


Author: Anthony Manning
Journal: Proc. Amer. Math. Soc. 133 (2005), 1693-1697
MSC (2000): Primary 37C70, 37C75, 37D20; Secondary 37D10, 37C27
Published electronically: January 13, 2005
MathSciNet review: 2120252
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Abstract: Suppose that $f$ and $f'$ are axiom A flows with attractors $A$ and $A'$. 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 $(h_t)$ sufficiently close to $(g_t)$ any attractor whose basin is not too thin is $\varepsilon$-dense in $A \times A'$.


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Additional Information

Anthony Manning
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email: akm@maths.warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07872-X
PII: S 0002-9939(05)07872-X
Received by editor(s): January 24, 2004
Published electronically: January 13, 2005
Communicated by: Michael Handel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.