Constructing subdivision rules from rational maps
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- by J. W. Cannon, W. J. Floyd and W. R. Parry
- Conform. Geom. Dyn. 11 (2007), 128-136
- DOI: https://doi.org/10.1090/S1088-4173-07-00167-1
- Published electronically: August 14, 2007
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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 $f^{\circ n}$ is the subdivision map of a finite subdivision rule. This enables one to give essentially combinatorial models for the dynamics of such iterates.References
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Bibliographic Information
- J. W. Cannon
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- Email: cannon@math.byu.edu
- W. J. Floyd
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
- MR Author ID: 67750
- Email: floyd@math.vt.edu
- W. R. Parry
- Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
- MR Author ID: 136390
- Email: walter.parry@emich.edu
- Received by editor(s): March 15, 2007
- Published electronically: August 14, 2007
- Additional Notes: This work was supported in part by NSF research grants DMS-0104030 and DMS-0203902.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 11 (2007), 128-136
- MSC (2000): Primary 37F10, 52C20; Secondary 57M12
- DOI: https://doi.org/10.1090/S1088-4173-07-00167-1
- MathSciNet review: 2329140