Shadowing and -limit sets of circular Julia sets
2013 ◽
Vol 35
(4)
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pp. 1045-1055
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AbstractIn this paper we consider quadratic polynomials on the complex plane${f}_{c} (z)= {z}^{2} + c$and their associated Julia sets,${J}_{c} $. Specifically, we consider the case that the kneading sequence is periodic and not an$n$-tupling. In this case${J}_{c} $contains subsets that are homeomorphic to the unit circle, usually infinitely many disjoint such subsets. We prove that${f}_{c} : {J}_{c} \rightarrow {J}_{c} $has shadowing, and we classify all$\omega $-limit sets for these maps by showing that a closed set$R\subseteq {J}_{c} $is internally chain transitive if, and only if, there is some$z\in {J}_{c} $with$\omega (z)= R$.
1996 ◽
Vol 144
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pp. 179-182
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Keyword(s):
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1969 ◽
Vol 35
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pp. 151-157
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2010 ◽
Vol 06
(07)
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pp. 1589-1607
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Keyword(s):
2001 ◽
Vol 04
(04)
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pp. 569-577
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2014 ◽
Vol 325
(3)
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pp. 1171-1178
2018 ◽
Vol 24
(1)
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pp. 20-33
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