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Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997. http://hdl.handle.net/2142/86942 Palmore, Julian Niamsup, Piyapong 2015-09-28T15:20:16Z 2015-09-28T15:20:16Z 10000-01-01 1997 1997 A complex analytic map f always decomposes the complex plane into two dis-joint subsets, the Julia set J(f) on which the family of iterates of f, $\{f\sp{k}\}\sbsp{k=0}{\infty}$, fails to be a normal family, and its complement, the Fatou set F(f). The dynamics of f on its Fatou set is relatively tame while the dynamics on its Julia set is always complicated. We study the Julia sets and Symbolic dynamics of certain rational and entire functions. We also estimate the size of some Julia sets in terms of their Hausdorff dimension. Made available in DSpace on 2015-09-28T15:20:16Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9717317.pdf: 2930473 bytes, checksum: 478b0106b0330269dde0d24203614fca (MD5) Previous issue date: 1997 Embargo set by: Seth Robbins for item 88223 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 77 p. (MiAaPQ)AAI9717317 eng Mathematics Julia Sets and Symbolic Dynamics of Certain Rational and Entire Functions text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.