Polynomial shift--like maps in $\mathbb{C}^k$

Sayani Bera

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arXiv · 1805.03142

Polynomial shift--like maps in $\mathbb{C}^k$

Sayani Bera

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Abstract

The purpose of this article is to explore a few properties of polynomial shift-like automorphisms of $\mathbb{C}^k.$ We first prove that a $\nu-$shift-like polynomial map (say $S_a$) degenerates essentially to a polynomial map in $\nu-$dimensions as $a \to 0.$ Secondly, we show that a shift-like map obtained by perturbing a hyperbolic polynomial (i.e., $S_a$, where $|a|$ is sufficiently small) has finitely many Fatou components, consisting of basins of attraction of periodic points and the component at infinity.

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Sayani Bera. 2018-05-08. Polynomial shift--like maps in $\mathbb{C}^k$. https://arxiv.org/abs/1805.03142

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