Type
Text
Type
Dissertation
Advisor
Martens, Marco | Lyubich, Mikhail | Bishop, Christopher | DeMarco, Laura.
Date
2016-12-01
Keywords
Mathematics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76376
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Infinitely renormalizable quadratic polynomials have been heavily studied. In the context of quadratic-like renormalization, one may try to prove the existence of a priori bounds, a definite thickness for the annuli corresponding to the renormalizations. In 1997, M. Lyubich showed that a priori bounds imply local connectivity of the Julia set and combinatorial rigidity for the corresponding quadratic polynomial. In a paper from 2006, J. Kahn showed that infinitely renormalizable quadratic polynomials of bounded primitive type admit a priori bounds. In 2002, H. Inou generalized some of the polynomial-like renormalization theory to polynomials of higher degree with several critical points. In my thesis, I generalize Kahn's theorem to the context of polynomials of higher degree admitting infinitely many primitive renormalizations of bounded type around each of their critical points. These a priori bounds imply local connectivity and rigidity. | 96 pages
Recommended Citation
Adams, Joseph, "Infinitely primitively renormalizable polynomials with bounded combinatorics" (2016). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2300.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2300