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arXiv · 1811.00617

Newhouse Laminations

Michael Benedicks·Marco Martens·Liviana Palmisano
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Abstract

Newhouse laminations occur in unfoldings of rank-one homoclinic tangencies. Namely, in these unfoldings, there exist codimension $2$ laminations of maps with infinitely many sinks which move simultaneously along the leaves. As consequence, in the space of real polynomial maps, there are examples of: H\'enon maps, in any dimension, with infinitely many sinks, quadratic H\'enon-like maps with infinitely many sinks and a period doubling attractor, quadratic H\'enon-like maps with infinitely many sinks and a strange attractor, non trivial analytic families of polynomial maps with infinitely many sinks.

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Michael Benedicks, Marco Martens, Liviana Palmisano. 2018-11-01. Newhouse Laminations. https://arxiv.org/abs/1811.00617

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