Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



Attractor sets and Julia sets in low dimensions

Author: A. Fletcher
Journal: Conform. Geom. Dyn. 23 (2019), 117-129
MSC (2010): Primary 30D05; Secondary 30C62, 30C65
Published electronically: June 25, 2019
MathSciNet review: 3973918
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $X$ is the attractor set of a conformal IFS (iterated function system) in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with a Julia set equal to $X$. We also show that in dimension two, with a further assumption similar to the open set condition, the same result can be achieved with a semigroup generated by one element. Consequently, in this case the attractor set is quasiconformally equivalent to the Julia set of a rational map.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30D05, 30C62, 30C65

Retrieve articles in all journals with MSC (2010): 30D05, 30C62, 30C65

Additional Information

A. Fletcher
Affiliation: Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115
MR Author ID: 749646

Received by editor(s): October 23, 2018
Received by editor(s) in revised form: March 6, 2019, and May 6, 2019
Published electronically: June 25, 2019
Additional Notes: This work was supported by a grant from the Simons Foundation (#352034, Alastair Fletcher).
Article copyright: © Copyright 2019 American Mathematical Society