{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Infinitely primitively renormalizable polynomials with bounded combinatorics","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76376"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"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."},{"label":"dcterms.available","value":"2017-09-20T16:50:08Z"},{"label":"dcterms.contributor","value":"Bishop, Christopher"},{"label":"dcterms.creator","value":"Adams, Joseph"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:08Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:08Z"},{"label":"dcterms.description","value":"Department of Mathematics"},{"label":"dcterms.extent","value":"96 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76376"},{"label":"dcterms.issued","value":"2016-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:08Z (GMT). No. of bitstreams: 1\nAdams_grad.sunysb_0771E_12819.pdf: 628158 bytes, checksum: ca8fdebb90ac122e307e7d2091a4a1aa (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Mathematics"},{"label":"dcterms.title","value":"Infinitely primitively renormalizable polynomials with bounded combinatorics"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/33%2F78%2F61%2F33786102961233922178630369264641839277/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/33%2F78%2F61%2F33786102961233922178630369264641839277","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}