2026-09-21T09:57:13Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/24082 2023-07-10 col_2142_16340 col_2142_5131 com_2142_16339 com_2142_8903 com_2142_5130

Kapovitch, Ilia Merenkov, Sergiy A. Kapovitch, Ilia Leininger, Christopher J. Athreya, Jayadev S. Kelsey, Gregory A. 2011-05-25T15:02:08Z 2011-05-25T15:02:08Z 2011-05-25T15:02:08Z 2011-05 In 2006, Bartholdi and Nekrashevych solved a decade-old problem in holomorphic dynamics by creatively applying the theory of self-similar groups. Nekrashevych expanded this work in 2009 to define what we refer to as mega-bimodules which capture the topological data of Hurwitz classes of topological polynomials. He also showed that proving that these mega-bimodules are sub-hyperbolic will have two important implications: that all iterated monodromy groups of topological polynomials are contracting and that the Hubbard- Schliecher spider algorithm for complex polynomials generalizes to topological polynomials. We prove sub- hyperbolicity in the simplest non-trivial case and apply these mega-bimodules to holomorphic dynamics to prove a partial converse to the Berstein-Levy Theorem proved in 1985. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-03-30T20:06:22Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 GAKThesis.tex: 143915 bytes, checksum: 97acdb7d3f278359d795539cf5fe846e (MD5) Kelsey_Gregory.pdf: 809019 bytes, checksum: 0a5a79e8739459a615642fe8a31904e6 (MD5) Made available in DSpace on 2011-05-25T15:02:08Z (GMT). No. of bitstreams: 4 Kelsey_Gregory.pdf: 793680 bytes, checksum: c70f8dbd8d4f35dd7b944a5962d6419b (MD5) license.txt: 4064 bytes, checksum: af7734958801e5f15c282ab1acb470e9 (MD5) GAKThesis.tex: 143915 bytes, checksum: 97acdb7d3f278359d795539cf5fe846e (MD5) 1_GAKThesis.tex: 143919 bytes, checksum: 9d94c0c7c13280b013b1e1f80243c13a (MD5) http://hdl.handle.net/2142/24082 en Copyright 2011 Gregory A. Kelsey Combinatorics of complex dynamics self-similar groups Mega-bimodules of topological polynomials: sub-hyperbolicity and Thurston obstructions Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD