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Recurrent critical points and typical limit sets of rational maps |
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| Authors: | Alexander M. Blokh John C. Mayer Lex G. Oversteegen |
| Affiliation: | Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170 ; Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170 ; Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170 |
| Abstract: | We consider a rational map  of the Riemann sphere with normalized Lebesgue measure  and show that if there is a subset of the Julia set  of positive  -measure whose points have limit sets not contained in the union of the limit sets of recurrent critical points, then  for  -a.e. point  and  is conservative, ergodic and exact. |
| Keywords: | Julia set complex analytic dynamics limit set recurrent critical point |
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