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International Journal of Mathematics and Mathematical Sciences - Volume 2004 2004, Issue 67, Pages 3685-3693



Department of Mathematics, University of Michigan, 2074 East Hall, Ann Arbor 48109-1109, MI, USA

Department of Mathematics and Statistics, Wichita State University, Wichita 67260-0033, KS, USA

Received 6 August 2002

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show that under some simple conditions a topological conjugacy h between two holomorphic self-maps f1 and f2 of complex n-dimensional projective space ℙn lifts canonically to a topological conjugacy H between the two corresponding polynomial self-maps of ℂn+1, and this conjugacy relates the two Green functions of f1 and f2. These conjugacies are interesting because their geometry is not inherited entirely from the geometry of the conjugacy on ℙn. Part of the geometry of such a conjugacy is given locally by a complex-valued function whose absolute value is determined by the Green functions for the two maps, but whose argument seems to appear out of thin air. We work out the local geometry of such conjugacies over the Fatou set and over Fatou varieties of the original map.





Author: John W. Robertson

Source: https://www.hindawi.com/



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