Type of Document	Master's Thesis
Author	Saenz Maldonado, Edgar Arturo
Author's Email Address	easaenzm@vt.edu
URN	etd-04302008-005312
Title	Brjuno Numbers and Complex Dynamics
Degree	Master of Science
Department	Mathematics
Advisory Committee	Advisor Name Title William J. Floyd Committee Chair Leslie D. Kay Committee Member Peter E. Haskell Committee Member
Keywords	Brjuno Numbers Siegel Disks Complex Dynamics
Date of Defense	2008-04-17
Availability	unrestricted
Abstract The 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 &alpha &isin R\Q, we also describe how the existence of a Siegel disk at the origin for the polynomial P(z) = exp(2&pi i&alpha)·(z − z²) implies the linearization of any germ of the form f(z) = exp(2&pi i&alpha)· z + Ord(z²).
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    MThesis.pdf 471.94 Kb 00:02:11 00:01:07 00:00:58 00:00:29 00:00:02

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