Blenders near polynomial product maps of \mathbb C²

2017/02/07 by Johan Taflin, Taflin, Johan
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.1702.02115

v2: add a result using a heterodimentional cycle between blenders

arxiv created 2017/07/26 · arxiv updated 2017/07/27

Abstract

In this paper we show that if p is a polynomial which bifurcates then the product map (z,w)↦(p(z),q(w)) can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types : repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets : the bifurcation locus of H_d(\mathbb P²) and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of Hénon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets.

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