Julia set

Known as: Julia fractal, Fatou set, Julia Sets 
In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets (Julia 'laces' and Fatou… (More)
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2018
2018
  • Christopher J. Bishop
  • 2018
We construct a transcendental entire function whose Julia set has locally finite 1-dimensional measure, hence Hausdorff dimension… (More)
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2011
2011
Bodil Branner and John Hubbard produced the first extensive study of iterated complex maps for cubic polynomials in Picard orbit… (More)
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2009
2009
We consider the basilica Julia set of the polynomial P (z) = z − 1 and construct all possible resistance (Dirichlet) forms, and… (More)
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2006
2006
Polynomial Julia sets have emerged as the most studied examples of fractal sets generated by a dynamical system. Apart from the… (More)
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2003
2003
In this paper, we give a proof of Sullivan’s complex bounds for the Feigenbaum quadratic polynomial and show that the Julia set… (More)
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Highly Cited
1998
Highly Cited
1998
It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c ∈ ∂M , the Julia set… (More)
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1997
1997
It is proved that non-exceptional rational functions f and g on the Riemann sphere have the same measure of maximal entropy ii… (More)
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1996
1996
Let ^ be the conformal isomorphism from the complement of the unit disc to the complement of the Mandelbrot set M. We study the… (More)
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Highly Cited
1993
Highly Cited
1993
KP = { z ∈ C | the sequence P ◦k(z) is bounded }. We will write Pc(z) = z2 + c, and Kc, etc., when discussing quadratic… (More)
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Highly Cited
1987
Highly Cited
1987
We show the Julia set of A sin(z) has positive area and the action of A sin(z) on its Julia set is not ergodic; the Julia set of… (More)
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