| dc.identifier.uri | http://hdl.handle.net/11401/76376 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.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. | |
| dcterms.available | 2017-09-20T16:50:08Z | |
| dcterms.contributor | Martens, Marco | en_US |
| dcterms.contributor | Lyubich, Mikhail | en_US |
| dcterms.contributor | Bishop, Christopher | en_US |
| dcterms.contributor | DeMarco, Laura. | en_US |
| dcterms.creator | Adams, Joseph | |
| dcterms.dateAccepted | 2017-09-20T16:50:08Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:08Z | |
| dcterms.description | Department of Mathematics | en_US |
| dcterms.extent | 96 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76376 | |
| dcterms.issued | 2016-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:08Z (GMT). No. of bitstreams: 1
Adams_grad.sunysb_0771E_12819.pdf: 628158 bytes, checksum: ca8fdebb90ac122e307e7d2091a4a1aa (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Mathematics | |
| dcterms.title | Infinitely primitively renormalizable polynomials with bounded combinatorics | |
| dcterms.type | Dissertation | |
