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On the Structure of Arithmetic Sums of Cantor Sets Associated with Series
This paper continues the investigation started in Anisca and Chlebovec (Nonlinearity 22:2127–2140, 2009). We exhibit conditions which imply that the...
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Embeddings of trees, cantor sets and solvable Baumslag–Solitar groups
We characterise when there exists a quasiisometric embedding between two solvable Baumslag–Solitar groups. This extends the work of Farb and Mosher...
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Reconstruction of a Coloring from its Homogeneous Sets
We study the following reconstruction problem for colorings. Given a countable set X (finite or infinite), a coloring on X is a function
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New Exotic Minimal Sets from Pseudo-Suspensions of Cantor Systems
We develop a technique, pseudo-suspension, that applies to invariant sets of homeomorphisms of a class of annulus homeomorphisms we describe,...
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On the multifractal measures: proportionality and dimensions of Moran sets
The aim of this work is to discuss the proportionality of the multifractal measures. We will prove that the ratio of the multifractal measures is...
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Local Trivializations of Suspended Minimal Cantor Systems and the Stable Orbit-Breaking Subalgebra
It is introduced an analogue of the orbit-breaking subalgebra for the case of free flows on locally compact metric spaces, which has a natural...
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Homogeneous isosceles-free spaces
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free...
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Comparison radius and mean topological dimension: Rokhlin property, comparison of open sets, and subhomogeneous C*-algebras
Let ( X , Γ) be a free minimal dynamical system, where X is a compact separable Hausdorff space and Γ is a discrete amenable group. It is shown that,...
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Isolated Diophantine Numbers
In this note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with the...
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Quasiconformal geometry and removable sets for conformal map**s
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain Ω ⊂ ℝ 2 that vanishes on a...
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Affine embeddings of Cantor sets in the plane
Let F , E ⊆ ℝ 2 be two self-similar sets. First, assuming F is generated by an IFS Ф with strong separation, we characterize the affrne maps g : ℝ 2 → ℝ 2 ...
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Sets, Functions, and Cardinality
A set is a collection of objects and a function is a rule to associate objects of two sets, where the terms “collection” and “rule” are well-defined...
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Calderón—Zygmund Operators and Commutators in Spaces of Homogeneous Type: Weighted Inequalities
The recent proof of the sharp weighted bound for Calderón-Zygmund operators has led to much investigation in sharp mixed bounds for operators and...
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Sets of Locally Finite Perimeter and Other Categories of Euclidean Sets
Here we discuss basic results from Geometric Measure Theory, including thick sets, the corkscrew condition, the geometric measure theoretic boundary,...
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Nonequilibrium Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps
Deterministic and time-reversible nonequilibrium molecular dynamics simulations typically generate “fractal” (fractional-dimensional) phase-space...
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