Type of Document Master's Thesis Author Saenz Maldonado, Edgar Arturo Author's Email Address email@example.com URN etd-04302008-005312 Title Brjuno Numbers and Complex Dynamics Degree Master of Science Department Mathematics Advisory Committee
Advisor Name Title Floyd, William J. Committee Chair Haskell, Peter E. Committee Member Kay, Leslie D. Committee Member Keywords
- Brjuno Numbers
- Siegel Disks
- Complex Dynamics
Date of Defense 2008-04-17 Availability unrestricted 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 &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).
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