Perturbing a Product of Stable Flows

نویسنده

  • ANTHONY MANNING
چکیده

Suppose that f and f ′ are axiom A flows with attractors A and A′. Then the attractor A×A′ for the product flow gt = ft×f ′ t on the product manifold is no longer hyperbolic (although there is a hyperbolic action of R2). It is easy to see that the attractor cannot explode but we show here that it cannot implode: for any flow (ht) sufficiently close to (gt) any attractor whose basin is not too thin is ε-dense in A× A′.

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تاریخ انتشار 2005