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dc.contributor.advisorVerma, Kaushal
dc.contributor.authorPal, Ratna
dc.date.accessioned2018-06-08T07:21:08Z
dc.date.accessioned2018-07-31T06:08:46Z
dc.date.available2018-06-08T07:21:08Z
dc.date.available2018-07-31T06:08:46Z
dc.date.issued2018-06-08
dc.date.submitted2015
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/3671
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/4541/G27321-Abs.pdfen_US
dc.description.abstractThesis 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. 1en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG27321en_US
dc.subjectHolomorphic Mappingen_US
dc.subjectHenon Mapsen_US
dc.subjectHolomorphic Automarphismen_US
dc.subjectHolomorphic endomarphismsen_US
dc.subjectComplex Manifoldsen_US
dc.subjectHénon Mapsen_US
dc.subjectGreen Functionsen_US
dc.subjectHolomorphic Mappingsen_US
dc.subject.classificationMathematicsen_US
dc.titleDynamical Properties of Families of Holomorphic Mappingsen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


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