Stable intersection of affine Cantor sets defined by two expanding maps
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DOI: 10.1016/j.jde.2018.08.023
Abstract: Abstract It is shown that in the context of affine Cantor sets with two increasing maps, the arithmetic sum of both of its elements is a Cantor set otherwise, it is a closure of countable… read more here.
Keywords: cantor; cantor sets; intersection affine; affine cantor ... See more keywords
Exact Hausdorff and Packing measure of certain Cantor sets, not necessarily self-similar or homogeneous
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DOI: 10.1016/j.jmaa.2019.01.036
Abstract: We compute the exact Hausdorff and packing measures of linear Cantor sets which might not be self similar or homogeneous . The calculation is based on the local behavior of the natural probability measure supported… read more here.
Keywords: self similar; exact hausdorff; cantor sets; hausdorff packing ... See more keywords
A new simple family of Cantor sets in R3 all of whose projections are one-dimensional
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DOI: 10.1016/j.topol.2020.107452
Abstract: Abstract In 1994, J. Cobb described a Cantor set in R 3 each of whose projections into 2-planes is one-dimensional. A series of works by other authors developing this field followed. We present another very… read more here.
Keywords: new simple; whose projections; cantor; cantor sets ... See more keywords
On intrinsic and extrinsic rational approximation to Cantor sets
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DOI: 10.1017/etds.2020.7
Abstract: We establish various new results on a problem proposed by Mahler [Some suggestions for further research. Bull. Aust. Math. Soc. 29 (1984), 101–108] concerning rational approximation to fractal sets by rational numbers inside and outside… read more here.
Keywords: rational approximation; cantor; cantor sets; fractal sets ... See more keywords
Volume of the hyperbolic cantor sets
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DOI: 10.1080/14689367.2019.1659754
Abstract: ABSTRACT In this paper, we study hyperbolic Cantor sets on the line. We prove that the Lebesgue measure of a hyperbolic Cantor set generated by a degree two expanding map satisfying a certain Zygmund condition… read more here.
Keywords: volume hyperbolic; cantor sets; hyperbolic cantor; cantor ... See more keywords
Diffusion on Middle-ξ Cantor Sets
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DOI: 10.3390/e20070504
Abstract: In this paper, we study Cζ-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard… read more here.
Keywords: middle cantor; cantor sets; diffusion middle; cantor ... See more keywords