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Some aspects of shift- like automorphisms of C-k

Bera, Sayani and Verma, Kaushal (2018) Some aspects of shift- like automorphisms of C-k. In: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 128 (1).

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Official URL: http://dx.doi.org/10.1007/s12044-018-0388-1

Abstract

The goal of this article is two fold. First, using transcendental shift-like automorphisms of C-k, k >= 3 we construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of C-k, k >= 3 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon-Esterle in C-2. The second example shows the existence of a Fatou-Bieberbach domain in C-k, k >= 3 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay-Rudin. In the second part we compute the order and type of entire mappings that parametrize one dimensional unstable manifolds for shift-like polynomial automorphisms and show how they can be used to prove a Yoccoz type inequality for this class of automorphisms.

Item Type: Journal Article
Additional Information: Copy right for this article belong to INDIAN ACAD SCIENCES, C V RAMAN AVENUE, SADASHIVANAGAR, P B #8005, BANGALORE 560 080, INDIA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 16 Apr 2018 20:09
Last Modified: 16 Apr 2018 20:09
URI: http://eprints.iisc.ac.in/id/eprint/59597

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