Rational maps whose Julia sets are Cantor circles
2013 ◽
Vol 35
(2)
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pp. 499-529
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AbstractIn this paper, we give a family of rational maps whose Julia sets are Cantor circles and show that every rational map whose Julia set is a Cantor set of circles must be topologically conjugate to one map in this family on their corresponding Julia sets. In particular, we give the specific expressions of some rational maps whose Julia sets are Cantor circles, but they are not topologically conjugate to any McMullen maps on their Julia sets. Moreover, some non-hyperbolic rational maps whose Julia sets are Cantor circles are also constructed.
2011 ◽
Vol 32
(5)
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pp. 1711-1726
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2013 ◽
Vol 23
(05)
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pp. 1350083
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1997 ◽
Vol 17
(2)
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pp. 253-267
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1992 ◽
Vol 12
(1)
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pp. 53-66
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1993 ◽
Vol 13
(1)
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pp. 167-174
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