The filled-in Julia set of a polynomial is : * a Julia set and its interior, * non-escaping set

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2016

2016

- Ahmed Mohammed, Arkan Jassim
- 2016

Fractal dimension is a measure of how fragmented of fractal object is. In fractal geometry, there are various approaches to… (More)

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2015

2015

- James W. Osborne
- 2015

Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider’s web fast escaping sets… (More)

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2008

2008

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an… (More)

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2008

2008

0 lies on a periodic orbit. We then perturb F0 by adding a pole at the origin. Our goal is to investigate the structure of the… (More)

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2007

2007

- Ilia Binder, Mark Braverman, Michael Yampolsky
- Foundations of Computational Mathematics
- 2007

We show that if a polynomial filled Julia set has empty interior, then it is computable.

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2007

2007

- Mark Braverman, Michael Yampolsky
- STOC
- 2007

While most polynomial Julia sets are computable, it has been recently shown [12] that there exist non-computable Julia sets. The… (More)

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2004

2004

- John W. Milnor
- Experimental Mathematics
- 2004

The operation of “mating” two suitable complex polynomial maps f1 and f2 constructs a new dynamical system by carefully pasting… (More)

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1998

1998

- Saeed Zakeri
- 1998

Let f : z 7→ z + c be a quadratic polynomial whose Julia set J is locallyconnected. We prove that the Brolin measure of the set… (More)

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1998

1998

- Saeed Zakeri
- 1998

We prove that the only possible biaccessible points in the Julia set of a Cremer quadratic polynomial are the Cremer fixed point… (More)

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Highly Cited

1993

Highly Cited

1993

- Rudolf Beran
- SIAM Review
- 1993

is connected. Otherwise, it has infinitely many pieces. The Mandelbrot set is the set of cvalues for which the filled Julia set… (More)

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