Invariant escaping Fatou components with two rank 1 limit functions for\n automorphisms of \ℂ²

2020/11/05 by Anna Miriam Benini, Alberto Saracco, Benini, Anna Miriam +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2011.02756

Abstract

We construct automorphisms of \ℂ², and more precisely\ntranscendental H 'enon maps, with an invariant escaping Fatou component which\nhas exactly two distinct limit functions, both of (generic) rank 1. We also\nprove a general growth lemma for the norm of points in orbits belonging to\ninvariant escaping Fatou components for automorphisms of the form\nF(z,w)=(g(z,w),z) with g(z,w):\ℂ²\→\ℂ\nholomorphic.\n

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