Abstract
We consider a rational mapping R(z) and use it to partition the sphere into two disjoint invariant sets, on one of which R(z) is well-behaved (the Fatou set), on the other of which R(z) has chaotic behavior (the Julia set). The first milestone of the theory is a theorem of Fatou and Julia that the repelling periodic points are dense in the Julia set. From this follows the homogeneous nature of the Julia set. In the words of Julia, “la structure de E’ est la même dans toutes ses parties.”
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Carleson, L., Gamelin, T.W. (1993). Basic Rational Iteration. In: Complex Dynamics. Universitext: Tracts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4364-9_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4364-9_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97942-7
Online ISBN: 978-1-4612-4364-9
eBook Packages: Springer Book Archive