Maximally and non-maximally fast escaping points of transcendental entire functions
2015 ◽
Vol 158
(2)
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pp. 365-383
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Keyword(s):
AbstractWe partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the intersection of the Julia set with the non-maximally fast escaping set is never empty. The proof uses a new covering result for annuli, which is of wider interest.It was shown by Rippon and Stallard that the fast escaping set has no bounded components. In contrast, by studying a function considered by Hardy, we give an example of a transcendental entire function for which the maximally and non-maximally fast escaping sets each have uncountably many singleton components.
2001 ◽
Vol 63
(3)
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pp. 367-377
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1997 ◽
Vol 122
(2)
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pp. 223-244
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2012 ◽
Vol 33
(4)
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pp. 1146-1161
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2000 ◽
Vol 20
(6)
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pp. 1577-1582
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Keyword(s):
1996 ◽
Vol 119
(3)
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pp. 513-536
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Keyword(s):
2018 ◽
Vol 40
(3)
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pp. 789-798
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2020 ◽
Vol 101
(3)
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pp. 453-465
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2016 ◽
Vol 34
(1-2)
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pp. 65-78
2004 ◽
Vol 14
(01)
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pp. 321-327
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