A STUDY OF THE DYNAMICS OF λ sin z
2002 ◽
Vol 12
(12)
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pp. 2869-2883
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Keyword(s):
Q Cycle
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This paper studies the dynamics of the family λ sin z for some values of λ. First we give a description of the Fatou set for values of λ inside the unit disc. Then for values of λ on the unit circle of parabolic type (λ = exp (i2πθ), θ = p/q, (p, q) = 1), we prove that if q is even, there is one q-cycle of Fatou components, if q is odd, there are two q cycles of Fatou components. Moreover the Fatou components of such cycles are bounded. For λ as above there exists a component Dq tangent to the unit disc at λ of a hyperbolic component. There are examples for λ such that the Julia set is the whole complex plane. Finally, we discuss the connectedness locus and the existence of buried components for the Julia set.
2016 ◽
Vol 37
(6)
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pp. 1997-2016
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Keyword(s):
2008 ◽
Vol 18
(04)
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pp. 1085-1100
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Keyword(s):
2008 ◽
Vol 18
(08)
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pp. 2309-2318
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Keyword(s):
2002 ◽
Vol 132
(3)
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pp. 531-544
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Keyword(s):
1967 ◽
Vol 29
◽
pp. 197-200
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2019 ◽
Vol 11
(1)
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pp. 5-17
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Keyword(s):
1995 ◽
Vol 05
(03)
◽
pp. 673-699
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Keyword(s):