Spiraling Domains in Dimension 2

I will present work in progress with Jasmin Raissy. We study the dynamics of polynomials maps of C^2 which are tangent to the identity at some fixed point. Our goal is to prove that there exist such maps for which the basin of attraction of the fixed point has infinitely many fixed connected components. This should be the case for the map (x,y)->(x+y^2+2x^2y,y+x^2+2y^2x)

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