Record Details

Dynamical Properties of Families of Holomorphic Mappings

Electronic Theses of Indian Institute of Science

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Field Value
 
Title Dynamical Properties of Families of Holomorphic Mappings
 
Creator Pal, Ratna
 
Subject Holomorphic Mapping
Henon Maps
Holomorphic Automarphism
Holomorphic endomarphisms
Complex Manifolds
Hénon Maps
Green Functions
Holomorphic Mappings
Mathematics
 
Description Thesis Abstract

In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical behavior of the composition of a pseudo-random sequence of H´enon mappings. In analogy with the dynamics of the iterates of a single H´enon map, it is possible to construct fibered Green functions that satisfy suitable invariance properties and the corresponding stable and unstable currents. Further, it is shown that the successive pullbacks of a suitable current by the skew H´enon maps converge to a multiple of the fibered stable current.
Second part of the thesis generalizes most of the above-mentioned results for a com- pletely random sequence of H´enon maps. In addition, for this random system of H´enon maps, we introduce the notion of average Green functions and average Green currents which carry many typical features of the classical Green functions and Green currents.
Third part consists of some results about the global dynamics of a special class of skew maps. To prove these results, we use the knowledge of dynamical behavior of pseudo- random sequence of H´enon maps widely. We show that the global skew map is strongly mixing for a class of invariant measures and also provide a lower bound on the topological entropy of the skew product.
We conclude the thesis by studying another class of maps which are skew products of holomorphic endomorphisms of Pk fibered over a compact base. We define the fibered Fatou components and show that they are pseudoconvex and Kobayashi hyperbolic.

















1
 
Contributor Verma, Kaushal
 
Date 2018-06-08T07:21:08Z
2018-06-08T07:21:08Z
2018-06-08
2015
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3671
http://etd.iisc.ernet.in/abstracts/4541/G27321-Abs.pdf
 
Language en_US
 
Relation G27321