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

Sayani Bera

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

Complex Variables 2018-10-02 v3 Dynamical Systems

Authors: Sayani Bera

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.

Keywords

holomorphic dynamics thurston maps polynomials over finite fields

Cite

@article{arxiv.1805.03142,
  title  = {Polynomial shift--like maps in $\mathbb{C}^k$},
  author = {Sayani Bera},
  journal= {arXiv preprint arXiv:1805.03142},
  year   = {2018}
}

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There is a considerable change in the results in addition to the change in title

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

Abstract

Keywords

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