Title page for ETD etd-04302008-005312

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
Floyd, William J. Committee Chair
Haskell, Peter E. Committee Member
Kay, Leslie D. Committee Member
  • Brjuno Numbers
  • Siegel Disks
  • Complex Dynamics
Date of Defense 2008-04-17
Availability unrestricted
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).

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