Brjuno Numbers and Complex Dynamics

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dc.contributor.authorSaenz Maldonado, Edgar Arturoen
dc.contributor.committeechairFloyd, William J.en
dc.contributor.committeememberKay, Leslie D.en
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:34:38Zen
dc.date.adate2008-05-14en
dc.date.available2014-03-14T20:34:38Zen
dc.date.issued2008-04-17en
dc.date.rdate2008-05-14en
dc.date.sdate2008-04-30en
dc.description.abstractThe Brjuno numbers play a fundamental role in the study of the 1-dimensional Complex Dynamics Theory. In this work we examine the proof of the Brjuno theorem by using elements of Number Theory. We also examine the topological version of the proof given by J. Yoccoz and his renormalization principle. If α ∈ ℝ\ℚ, we also describe how the existence of a Siegel disk at the origin for the polynomial P(𝑧) = exp(2πiα)·(𝑧 − 𝑧²) implies the linearization of any germ of the form 𝑓(𝑧) = exp(2πiα)·𝑧 + 𝑂(𝑧²).en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-04302008-005312en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04302008-005312/en
dc.identifier.urihttp://hdl.handle.net/10919/32055en
dc.publisherVirginia Techen
dc.relation.haspartMThesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectBrjuno Numbersen
dc.subjectSiegel Disksen
dc.subjectComplex Dynamicsen
dc.titleBrjuno Numbers and Complex Dynamicsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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