Related papers: On measures and semiconjugacies for affine interva…

In this paper, we obtain new bounds for the Hausdorff dimension of planar elliptic measure via the application of quasiconformal mappings, with these bounds depending solely on the ellipticity constant of the matrix. In fact, in our case…

We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…

Every equi-isoclinic tight fusion frame (EITFF) is a type of optimal code in a Grassmannian, consisting of subspaces of a finite-dimensional Hilbert space for which the smallest principal angle between any pair of them is as large as…

For $i = 0, 1, 2, \dots, k$, let $\mu_i$ be a Borel probability measure on $[0,1]$ which is equivalent to Lebesgue measure $\lambda$ and let $T_i:[0,1] \rightarrow [0,1]$ be $\mu_i$-preserving ergodic transformations. We say that…

For integers $a$ and $b\geq 2$, let $T_a$ and $T_b$ be multiplication by $a$ and $b$ on $\mathbb{T}=\mathbb{R}/\mathbb{Z}$. The action on $\mathbb{T}$ by $T_a$ and $T_b$ is called $\times a,\times b$ action and it is known that, if $a$ and…

In this paper, we study invariant Einstein metrics on Ledger-Obata spaces $F^m/\operatorname{diag}(F)$. In particular, we classify invariant Einstein metrics on $F^4/\operatorname{diag}(F)$ and estimate the number of invariant Einstein…

Let $d >1$. In this paper we show that for an irreducible permutation $\pi$ which is not a rotation, the set of $[\lambda]\in \mathbb{P}_+^{d-1}$ such that the interval exchange transformation $f([\lambda],\pi)$ is not weakly mixing does…

$\theta$ intermediate dimensions are a continuous family of dimensions that interpolate between Hausdorff and Box dimensions of fractal sets. In this paper we study the problem of the relationship between the dimension of a set…

We consider the homogeneous space $M=H\times H/\Delta K$, where $H/K$ is an irreducible symmetric space and $\Delta K$ denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of $H\times H$-invariant…

In this paper it is shown that if $E\subset\mathbb R^{n+1}$ is an $s$-AD regular compact set, with $s\in [n-\frac12,n)$, and $E$ is contained in a hyperplane or, more generally, in an $n$-dimensional $C^1$ manifold, then the Hausdorff…

The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP…

We prove a structure theorem for any $n$-rectifiable set $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, satisfying a weak version of the lower ADR condition, and having locally finite $H^n$ ($n$-dimensional Hausdorff) measure. Namely, that…

The model of homogeneous semicoherent interphase boundary describes the processes of absorption and thermoactivated migration of irradiation-produced inequilibrium point defects at a semicoherent boundary between a heterophase precipitate…

We investigate the quantum dynamics of wave packets in a class of decorated lattices, both quasiperiodic and random, where a nominal quasi-one dimensionality is introduced at local levels, bringing in a deterministic or even random…

Let $\mathfrak a$ be an algebraic Lie algebra. An adapted pair for $\mathfrak a$ is pair $(h,\eta)$ consisting of an ad-semisimple element of $h \in \mathfrak a$ and a regular element of $\eta \in \mathfrak a^*$ satisfying $(ad \…

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a…

We present shrinking targets results for general systems with the emphasis on applications for IETs (interval exchange transformations) $(J,T)$, $J=[0,1)$. In particular, we prove that if an IET $(J,T)$ is ergodic (relative to the Lebesgue…

Using the self-contained PDE analysis, this paper investigates the existence and the decay properties of the invariant measure in elliptic homogenization of non-divergence form with an interface assumptions on the leading coefficient $A$…

We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the…

We consider an infinite extension $K$ of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. $K$ is equipped with an inductive limit topology; its conjugate $\bar{K}$ is a completion of $K$…