Buried Sierpinski curve Julia sets
Robert L. Devaney Daniel M. Look
Discrete & Continuous Dynamical Systems - A 2005, 13(4): 1035-1046 doi: 10.3934/dcds.2005.13.1035
In this paper we prove the existence of a new type of Sierpinski curve Julia set for certain families of rational maps of the complex plane. In these families, the complementary domains consist of open sets that are preimages of the basin at $\infty$ as well as preimages of other basins of attracting cycles.
keywords: Julia sets rational map. Sierpinski curve
Accessible points in the Julia sets of stable exponentials
Ranjit Bhattacharjee Robert L. Devaney R.E. Lee Deville Krešimir Josić Monica Moreno-Rocha
Discrete & Continuous Dynamical Systems - B 2001, 1(3): 299-318 doi: 10.3934/dcdsb.2001.1.299
In this paper we consider the question of accessibility of points in the Julia sets of complex exponential functions in the case where the exponential admits an attracting cycle. In the case of an attracting fixed point it is known that the Julia set is a Cantor bouquet and that the only points accessible from the basin are the endpoints of the bouquet. In case the cycle has period two or greater, there are many more restrictions on which points in the Julia set are accessible. In this paper we give precise conditions for a point to be accessible in the periodic point case in terms of the kneading sequence for the cycle.
keywords: Accessibility Julia sets. cantor bouquets

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