Attractors for graph critical rational maps

Authors:
Alexander Blokh and Michal Misiurewicz

Journal:
Trans. Amer. Math. Soc. **354** (2002), 3639-3661

MSC (2000):
Primary 37F10; Secondary 37E25

DOI:
https://doi.org/10.1090/S0002-9947-02-02999-9

Published electronically:
April 30, 2002

MathSciNet review:
1911515

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Abstract | References | Similar Articles | Additional Information

Abstract: We call a rational map *graph critical* if any critical point either belongs to an invariant finite graph , or has minimal limit set, or is non-recurrent and has limit set disjoint from . We prove that, for any conformal measure, either for almost every point of the Julia set its limit set coincides with , or for almost every point of its limit set coincides with the limit set of a critical point of .

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Additional Information

**Alexander Blokh**

Affiliation:
Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060

Email:
ablokh@math.uab.edu

**Michal Misiurewicz**

Affiliation:
Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216

Email:
mmisiure@math.iupui.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-02999-9

Keywords:
Complex dynamics,
attractors,
conformal measures,
postcritical set

Received by editor(s):
July 7, 2000

Received by editor(s) in revised form:
December 20, 2001

Published electronically:
April 30, 2002

Additional Notes:
The first author was partially supported by NSF grant DMS 9970363

The second author was partially supported by NSF grant DMS 9970543

Article copyright:
© Copyright 2002
American Mathematical Society