Keywords
rational maps, subdivision rules
Abstract
This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f is the subdivision map of a finite subdivision rule. This enables one to give essentially combinatorial models for the dynamics of such iterates.
Original Publication Citation
Cannon, J. W., Floyd, W. J., Parry, W. R., Constructing subdivision rules from rational maps, Conform. Geom. Dyn. 11 (27), 128-136.
BYU ScholarsArchive Citation
Cannon, J. W.; Floyd, W. J.; and Parry, W. R., "Constructing subdivision rules from rational maps" (2007). Faculty Publications. 241.
https://scholarsarchive.byu.edu/facpub/241
Document Type
Peer-Reviewed Article
Publication Date
2007-08-14
Permanent URL
http://hdl.lib.byu.edu/1877/1481
Publisher
The American Mathematical Society
Language
English
College
Physical and Mathematical Sciences
Department
Mathematics
Copyright Status
© 2007 American Mathematical Society
Copyright Use Information
http://lib.byu.edu/about/copyright/