Bera, Sayani and Pal, Ratna and Verma, Kaushal (2017) Examples of non-autonomous basins of attraction. In: Illinois Journal of Mathematics, 61 (3-4). pp. 531-567. ISSN 0019-2082
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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 k ≥ 3, there exist (k − 1) mutually disjoint Short ℂk ’s in ℂkk. 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.
| Item Type: | Journal Article |
|---|---|
| Publication: | Illinois Journal of Mathematics |
| Publisher: | University of Illinois |
| Additional Information: | The Copyright of this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 17 Jun 2022 07:35 |
| Last Modified: | 17 Jun 2022 07:35 |
| URI: | https://eprints.iisc.ac.in/id/eprint/73516 |
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