Attractors for graph critical rational maps |
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| Authors: | Alexander Blokh Michal Misiurewicz |
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| Institution: | Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060 ; Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216 |
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| 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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| Keywords: | Complex dynamics attractors conformal measures postcritical set |
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