منابع مشابه
A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions
Although numerous computer programs have been written to compute sets of points which claim to approximate Julia sets, no reliable high precision pictures of nontrivial Julia sets are currently known. Usually, no error estimates are added and even those algorithms which work reliable in theory, become unreliable in practice due to rounding errors and the use of fixed length floating point numbe...
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In this paper, we consider the family of rational maps Fλ(z) = z n + λ zd , where n ≥ 2, d ≥ 1, and λ ∈ C. We consider the case where λ lies in the main cardioid of one of the n − 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps Fλ and Fμ are conjugate on these Julia sets only if the parameters at the center...
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If the preimage of a four-point set under a meromorphic function belongs to the real line then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if the Julia set of a rational function is contained in a smooth curve then it is contained in a circle. If the full preimage of a two-point set under a rational...
متن کاملConnectivity of Julia Sets for Singularly Perturbed Rational Maps
In this paper we consider the family of rational maps of the form F λ (z) = z n + λ/z n where n ≥ 2. It is known that there are two cases where the Julia sets of these maps are not connected. If the critical values of F λ lie in the basin of ∞, then the Julia set is a Cantor set. And if the critical values lie in the preimage of the basin surrounding the pole at 0, then the Julia set is a Canto...
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We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1988
ISSN: 0196-8858
DOI: 10.1016/0196-8858(88)90007-3