490 research outputs found
Moran Sets and Hyperbolic Boundaries
In the paper, we prove that a Moran set is homeomorphic to the hyperbolic
boundary of the representing symbolic space in the sense of Gromov, which
generalizes the results of Lau and Wang [Indiana U. Math. J. {\bf 58} (2009),
1777-1795]. Moreover, by making use of this, we establish the Lipschitz
equivalence of a class of Moran sets.Comment: 14 pages, 1 figur
Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
In the paper, we focus on the connectedness of planar self-affine sets
generated by an integer expanding matrix with and a collinear digit set , where and
such that is linearly independent. We discuss
the domain of the digit to determine the connectedness of
. Especially, a complete characterization is obtained when
we restrict to be an integer. Some results on the general case of are obtained as well.Comment: 15 pages, 10 figure
On the connectedness of planar self-affine sets
In this paper, we consider the connectedness of planar self-affine set
arising from an integral expanding matrix with
characteristic polynomial and a digit set
. The necessary and sufficient conditions only
depending on are given for the to be connected.
Moreover, we also consider the case that is non-consecutively
collinear.Comment: 18 pages; 18 figure
Topological Structure of Fractal Squares
Given an integer and a digit set , there is a self-similar set satisfying
the set equation: . We call such a fractal square. By
studying a periodic extension , we classify into three
types according to their topological properties. We also provide some simple
criteria for such classification.Comment: 17 pages, 12 figure
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