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Miles, Joseph B. Kline, Bradford J. 2011-05-07T13:22:56Z 2011-05-07T13:22:56Z 10000-01-01 1995 We prove a global result for rational functions that is analogous to a local theorem of L. E. Boettcher (1904). Under the hypotheses that f is a complex rational function with a superattractive fixed point $\alpha$ of order $p \ge 2$ and that $\alpha$ is the only critical point of f in the immediate basin of attraction of $\alpha,$ we prove that there exists a conformal map $w = \varphi(z)$ of the entire immediate basin of attraction of $\alpha$ onto the unit disk such that $(\varphi \circ f \circ \varphi\sp{-1})(w) = w\sp{p}.$ In our proof, the conjugating function $\varphi$ appears as the unique fixed point of a certain contraction operator on a complete metric space of one-to-one analytic functions. We make extensive use of the topological concept of a branched covering space in defining the contraction operator and, hence, in obtaining the global existence of $\varphi.$ Made available in DSpace on 2011-05-07T13:22:56Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543631.pdf: 1846358 bytes, checksum: 33e97bfc74cb318ca00469ce264701e8 (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:01Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:25:03-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9543631 (UMI)AAI9543631 http://hdl.handle.net/2142/21910 eng Copyright 1995 Kline, Bradford J. Mathematics A global Boettcher's theorem text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.