Brjuno Numbers and Complex Dynamics

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 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).

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2008

Author dc:creator

• Saenz Maldonado, Edgar Arturo

Chair dc:contributor.committeechair

• Floyd, William J.

Committee members dc:contributor.committeemember

• Kay, Leslie D.
• Haskell, Peter E.

• Brjuno Numbers
• Siegel Disks
• Complex Dynamics

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-04302008-005312

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32055