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Permutable entire functions and their Julia sets
Published online by Cambridge University Press: 26 October 2001
Abstract
In 1922–23, Julia and Fatou proved that any 2 rational functions f and g of degree at least 2 such that f(g(z)) = g(f(z)), have the same Julia set. Baker then asked whether the result remains true for nonlinear entire functions. In this paper, we shall show that the answer to Baker's question is true for almost all nonlinear entire functions. The method we use is useful for solving functional equations. It actually allows us to find out all the entire functions g which permute with a given f which belongs to a very large class of entire functions.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 1 , July 2001 , pp. 129 - 138
- Copyright
- 2001 Cambridge Philosophical Society
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