Open Access
Fall and Winter 2017 Examples of non-autonomous basins of attraction
Sayani Bera, Ratna Pal, Kaushal Verma
Illinois J. Math. 61(3-4): 531-567 (Fall and Winter 2017). DOI: 10.1215/ijm/1534924839

Abstract

The purpose of this paper is to present several examples of non-autonomous basins of attraction that arise from sequences of automorphisms of Ck. In the first part, we prove that the non-autonomous basin of attraction arising from a pair of automorphisms of C2 of a prescribed form is biholomorphic to C2. This, in particular, provides a partial answer to a question raised in (A survey on non-autonomous basins in several complex variables (2013) Preprint) in connection with Bedford’s Conjecture about uniformizing stable manifolds. In the second part, we describe three examples of Short Ck’s with specified properties. First, we show that for k3, there exist (k1) mutually disjoint Short Ck’s in Ck. Second, we construct a Short Ck, large enough to accommodate a Fatou–Bieberbach domain, that avoids a given algebraic variety of codimension 2. Lastly, we discuss examples of Short Ck’s with (piece-wise) smooth boundaries.

Citation

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Sayani Bera. Ratna Pal. Kaushal Verma. "Examples of non-autonomous basins of attraction." Illinois J. Math. 61 (3-4) 531 - 567, Fall and Winter 2017. https://doi.org/10.1215/ijm/1534924839

Information

Received: 5 December 2017; Revised: 25 May 2018; Published: Fall and Winter 2017
First available in Project Euclid: 22 August 2018

zbMATH: 06932516
MathSciNet: MR3845733
Digital Object Identifier: 10.1215/ijm/1534924839

Subjects:
Primary: 32H02
Secondary: 32H50

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

Vol.61 • No. 3-4 • Fall and Winter 2017
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