Show simple item record

dc.contributor.advisorChairperson, Graduate Committee: Lukas Geyeren
dc.contributor.authorManlove, Joseph Michaelen
dc.description.abstractThe results presented here answers in part a conjecture of Douady about sharpness of the Brjuno condition. Douady hypothesized that a Siegel disk exists for a rational function if and only if the Brjuno condition is satisfied by the rotation number. It is known that the Brjuno condition is sharp for quadratic polynomials and many special families. This thesis focuses on a class of rational functions, many of which have not been considered previously. Specific examples of maps for which these results apply include quadratic rational maps with an attracting cycle. Also included are those rational functions arising of Newton's method on cubic polynomials with distinct roots.en
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.subject.lcshFatou setsen
dc.subject.lcshRational equivalence (Algabraic geometry)en
dc.titleAllowable rotation numbers for siegel disks of rational mapsen
dc.rights.holderCopyright 2015 by Joseph Michael Manloveen
thesis.catalog.ckey2759028en, Graduate Committee: Jaroslaw Kwapisz; Marcy Barge; Kevin Wildrick; David Ayalaen Sciences.en

Files in this item


This item appears in the following Collection(s)

Show simple item record

MSU uses DSpace software, copyright © 2002-2017  Duraspace. For library collections that are not accessible, we are committed to providing reasonable accommodations and timely access to users with disabilities. For assistance, please submit an accessibility request for library material.