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Visible and invisible Cantor sets
(Birkhauser Boston Inc, 2012)
In this chapter we study for which Cantor sets there exists a gauge-function h, such that the h−Hausdorff measure—is positive and finite. We show that the collection of sets for which this is true is dense in the set of ...
On distance sets, box-counting and Ahlfors regular sets
(Alliance of Diamond Open Access Journals, 2017-05)
We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent s > 1. As a corollary, we improve upon a recent result of Orponen, by showing that if A ...
Improved bounds for the dimensions of planar distance sets
(European Mathematical Society, 2020-12)
We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than 1, improving recent estimates of Keleti and Shmerkin, and of Liu in ...
On the Hausdorff dimension of pinned distance sets
(Hebrew Univ Magnes Press, 2019-04-17)
We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension ...
Assouad dimension and local structure of self-similar sets with overlaps in Rd
(Academic Press Inc Elsevier Science, 2020-08)
For a self-similar set in Rd that is the attractor of an iterated function system that does not verify the weak separation property, Fraser, Henderson, Olson and Robinson showed that its Assouad dimension is at least 1. ...
Characterizations of Postman Sets
(Elsevier Science B. V., 2004-12)
Using results by McKee and Woodall on binary matroids, we prove that the set of postman sets has odd cardinality, generalizing a result by Toida on the cardinality of cycles in Eulerian graphs. We study the relationship ...
Characterizations of postman sets
(Elsevier Science, 2008-06)
Using results by McKee and Woodall on binary matroids, we show that the set of postman sets has odd cardinality, generalizing a result by Toida on the cardinality of cycles in Eulerian graphs. We study the relationship ...
Assouad dimensions of complementary sets
(Royal Society of Edinburgh, 2018-07)
Given a positive, decreasing sequence a, whose sum is L, we consider all the closed subsets of [0, L] such that the lengths of their complementary open intervals are in one-to-one correspondence with the sequence a. The ...
Characterization and computation of control invariant sets within target regionsfor linear impulsive control systems
(Cornell University, 2021-03)
Linear impulsively controlled systems are suitable to describe a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they remain uncontrolled for ...
Classifying cantor sets by their fractal dimensions
(American Mathematical Society, 2010-11)
In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-packing measures, for the family of dimension ...