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Constructing subdivision rules from rational maps
Author(s):
J.
W.
Cannon;
W.
J.
Floyd;
W.
R.
Parry
Journal:
Conform. Geom. Dyn.
11
(2007),
128-136.
MSC (2000):
Primary 37F10, 52C20;
Secondary 57M12
Posted:
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  is a critically finite rational map with no periodic critical points, then for any sufficiently large integer  the iterate  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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- 1.
- M. Bonk and D. Meyer, Topological rational maps and subdivisions, in preparation.
- 2.
- J. W. Cannon, W. J. Floyd, and W. R. Parry, Finite subdivision rules, Conform. Geom. Dyn. 5 (2001), 153-196 (electronic). MR 1875951 (2002j:52021)
- 3.
- J. W. Cannon, W. J. Floyd, R. Kenyon, and W. R. Parry, Constructing rational maps from subdivision rules, Conform. Geom. Dyn. 7 (2003), 76-102 (electronic). MR 1992038 (2004f:37062)
- 4.
- J. W. Cannon, W. J. Floyd, and W. R. Parry, Expansion complexes for finite subdivision rules I, Conform. Geom. Dyn. 10 (2006), 63-99 (electronic). MR 2218641 (2007c:30048)
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Additional 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
Email:
floyd@math.vt.edu
W.
R.
Parry
Affiliation:
Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email:
walter.parry@emich.edu
DOI:
10.1090/S1088-4173-07-00167-1
PII:
S 1088-4173(07)00167-1
Keywords:
Finite subdivision rule,
rational map,
conformality
Received by editor(s):
March 15, 2007
Posted:
August 14, 2007
Additional Notes:
This work was supported in part by NSF research grants DMS-0104030 and DMS-0203902.
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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