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### Open Access Journals

DCDS

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.

DCDS-B

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.

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