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Shift-like Automorphisms of Ck

Electronic Theses of Indian Institute of Science

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Title Shift-like Automorphisms of Ck
 
Creator Bera, Sayani
 
Subject Automorphisms
Endomorphism
Polynomial Shift-Like Maps
Unstable Manifolds
Yoccoz Inequality
Manifolds (Mathematics)
Mappings (Mathematics)
Polynomial Automorphisms
Polynomial Shifts
Mathematics
 
Description We use transcendental shift-like automorphisms of Ck, k > 2 to construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon-Esterle in C2. The second example shows the existence of a Fatou-Bieberbach domain in Ck,k > 2 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.
 
Contributor Verma, Kaushal
 
Date 2018-01-02T20:49:17Z
2018-01-02T20:49:17Z
2018-01-03
2014
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/2959
http://etd.ncsi.iisc.ernet.in/abstracts/3821/G26702-Abs.pdf
 
Language en_US
 
Relation G26702