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Infinitely primitively renormalizable polynomials with bounded combinatorics

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dc.contributor.advisor Lyubich, Mikhail en_US
dc.contributor.author Adams, Joseph en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:08Z
dc.date.available 2017-09-20T16:50:08Z
dc.date.issued 2016-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76376 en_US
dc.description 96 pgs en_US
dc.description.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. en_US
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 en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.title Infinitely primitively renormalizable polynomials with bounded combinatorics en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Martens, Marco en_US
dc.contributor.committeemember Bishop, Christopher en_US
dc.contributor.committeemember DeMarco, Laura en_US

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