Related papers: Massive Helson sets

We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem

In this work, the classical Borsuk conjecture is discussed, which states that any set of diameter 1 in the Euclidean space $ {\mathbb R}^d $ can be divided into $ d+1 $ parts of smaller diameter. During the last two decades, many…

This article consists in applications of [arXiv:2511.14232] in the case of homemomorphisms of higher genus surfaces whose homological rotation set is big enough -- a class of dynamics that is open. We first prove a structure theorem for the…

We prove that for k an uncountable cardinal, there exist 2^k many non homeomorphic weakly compact convex subsets of weight k in the Hilbert space of density k.

We compare limit-based and scale-local dimensions of complex distributions, particularly for a strange attractor of the Henon map. Scale-local dimensions as distributions on scale are seen to exhibit a wealth of detail. Limit-based…

We show that, almost surely, the Hausdorff dimension $s_0$ of a random covering set is preserved under all orthogonal projections to linear subspaces with dimension $k>s_0$. The result holds for random covering sets with a generating…

We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we…

We prove that subsets of ${\Bbb R}^d$, $d \ge 4$ of large enough Hausdorff dimensions contain vertices of an equilateral triangle. It is known that additional hypotheses are needed to assure the existence of equilateral triangles in two…

We prove that the k-medial axis of an arbitrary closed set in Rn is n-k+1-rectifiable (and hence of dimension at most n-k+1). This result gives a first stratification for medial axis of any closed set, which has been widely studied and used…

In this paper we consider Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including $A$-coupled expanding systems. We prove that Li-Yorke pairs of $A$- coupled-expanding system under some conditions have…

We give a definition of thickness in $\mathbb{R}^d$ that is useful even for totally disconnected sets, and prove a Gap Lemma type result. We also guarantee an interval of distances in any direction in thick compact sets, relate thick sets…

In this paper, we study multi-rotation orbits on the unit circle. We obtain a natural generalization of a classical result which says that orbits of irrational rotations on the unit circle are dense. It is possible to show that this result…

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…

We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of…

We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in $\mathbb{R}^n$. As an application, we find an upper bound close to $n-k$ for the Hausdorff dimension of sets with large $k$-porosity. With $k$-porous sets we…

We prove the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3. In dimension 5 we obain somewhat sharper results. There are examples where the number of effective…

In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from…

If the system S of contracting similitudes on $ R^2$ satisfies open convex set condition, then the set F of extreme points of the convex hull $\tilde{K}$ of it's invariant self-similar set K has Hausdorff dimension 0 . If, additionally, all…

The set of badly approximable numbers, Bad, is known to be winning for Schmidt's game and hence has full Hausdorff dimension. It is also known that the set of inhomogeneously badly approximable numbers has full dimension. We prove that the…

We study one dimensional sets (Hausdorff dimension) lying in a Hilbert space. The aim is to classify subsets of Hilbert spaces that are contained in a connected set of finite Hausdorff length. We do so by extending and improving results of…