International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 436827 | https://doi.org/10.1155/S0161171204208031

John W. Robertson, "The geometry of some natural conjugacies in n dynamics", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 436827, 9 pages, 2004. https://doi.org/10.1155/S0161171204208031

The geometry of some natural conjugacies in n dynamics

Received06 Aug 2002

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 n lifts canonically to a topological conjugacy H between the two corresponding polynomial self-maps of n+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 n. 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.

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.


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