On the dynamics of nondegenerate polynomial endomorphisms in two dimensions.
Item
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Title
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On the dynamics of nondegenerate polynomial endomorphisms in two dimensions.
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Identifier
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AAI9807982
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identifier
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9807982
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Creator
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Peng, Guiai.
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Contributor
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Adviser: Dennis Sullivan
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Date
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1997
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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The main purpose of this work is to investigate the dynamics of non-degenerate polynomial endomorphisms of {dollar}\doubc\sp2{dollar} (A polynomial endomorphism of {dollar}\doubc\sp2{dollar} is said to be nondegenerate if it can be holomorphically extended to {dollar}\IP\sp2).{dollar} It is shown that if the restriction to the line at infinity of a nondegenerate polynomial endomorphism p of {dollar}\doubc\sp2{dollar} is hyperbolic, then p is conjugate to its highest homogeneous term restricted to the intersection of the Julia set {dollar}{lcub}\cal J{rcub}(p){dollar} and a neighbourhood of the line at infinity. We describe the geometric structure of the Julia set and the canonical current associated with p near the line at infinity. We also generalize the Brolin-Lyubich theorem for any nondegenerate polynomial endomorphism of {dollar}\doubc\sp2.{dollar}.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
