Related papers: Assouad-type Dimensions of Overlapping Self-affine…
We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincar\'e inequality. For foliations of a metric space X defined by a…
A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and…
We introduce the mean Assouad dimension of a dynamical system, motivated by the Assouad dimension in fractal geometry. Using dimension interpolation, we further define the mean Assouad spectrum. This provides a new family of bi-Lipschitz…
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…
In this paper we compute the Assouad and lower spectra of Bedford--McMullen sponges in $\mathbb{R}^3$ explicitly. According to the formulae established, we discover that the spectra are not determined by the ratio set, and the box, lower…
A range of bosonic models can be expressed as (sometimes generalized) $\sigma$-models, with equations of motion coming from a selfduality constraint. We show that in D=2, this is easily extended to supersymmetric cases, in a superspace…
We propose a new spontaneous supersymmetry breaking mechanism, in which extra compact dimensions play an important role. To illustrate our mechanism, we study a simple model consisting of two chiral superfields, where one spatial dimension…
In this paper we study systems of autonomous algebraic ODEs in several differential indeterminates. We develop a notion of algebraic dimension of such systems by considering them as algebraic systems. Afterwards we apply differential…
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…
We define $(\alpha_n)$ -regular sets in uniformly perfect metric spaces. This definition is quasisymmetrically invariant and the construction resembles generalized dyadic cubes in metric spaces. For these sets we then determine the…
In this note, we provide equivalent definitions for fractal geometric dimensions through dyadic cube constructions. Given a metric space $X$ with finite Assouad dimension, i.e., satisfying the doubling property, we show that the…
In the paper, we define a class of new fractals named ``non-autonomous attractors", which are the generalization of classic Moran sets and attractors of iterated function systems. Simply to say, we replace the similarity mappings by…
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensions: a family of dimensions depending on a parameter $\theta…
We study the packing dimension of Borel measures under orthogonal projections. We give a necessary and sufficient condition such that typical projections of Borel probability measures have full packing dimension and derive general lower…
Let $(\Sigma, \sigma)$ be a dynamical system, and let $U\subset \Sigma$. Consider the survivor set \[ \Sigma_U=\{x\in \Sigma\mid \sigma^n(x)\notin U\textrm{for all}n\} \] of points that never enter the subset $U$. We study the size of this…
We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial positive answer to the question of Falconer. We also study…
We study the growth of norms of ergodic integrals for the translation action on spaces coming from expansive, self-affine Delone sets. The linear map giving the self-affinity induces a renormalization map on the pattern space and we show…
Optimal quasiconformal dimension distortions bounds for subsets of the complex plane have been established by Astala. We show that these estimates can be improved when one considers subsets of the real line of arbitrary Hausdorff dimension.…
The class of the two-axes pseudo-Finslerian metrics which is specified by the condition of the angle-separation in the involved characteristic functions is proposed and studied. The complete Total Set of algebraic and differential equations…
We construct supersymmetric Q-balls and boson stars in (d+1) dimensions. These non-topological solitons are solutions of a scalar field model with global U(1) symmetry and a scalar field potential that appears in gauge-mediated…