相关论文: Separation conditions on controlled Moran construc…

An analysis of necessary conditions for the existence of controlled dynamics with an attractor of a specified topological type is given. It uses the Hopf classification by degree for Gauss maps of manifolds to spheres of the same dimension,…

We discuss conditions under which certain compactifications of topological spaces can be obtained by composing the ultrafilter space monad with suitable reflectors. In particular, we show that these compactifications inherit their…

In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable…

This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain…

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction…

It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…

Pressure-dependent transmittance and reflectance spectra of TiOBr and TiOCl single crystals at room temperature suggest the closure of the Mott-Hubbard gap, i.e., the gap is filled with additional electronic states extending down to the…

Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-affine proper subsets of the original set. These self-affine…

We construct a probability measure $\mu$ supported on a set of zero $2d/p$-Hausdorff measure such that $\hat{\mu}\in L_{p}(\mathbb{R}^d)$.

The topological classifications of quadratic bosonic systems according to the symmetries of the dynamic matrices from the equations of motion of closed systems and the effective Hamiltonians from the Lindblad equations of open systems are…

We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with…

Given some set, how hard is it to construct a measure supported by it? We classify some variations of this task in the Weihrauch lattice. Particular attention is paid to Frostman measures on sets with positive Hausdorff dimension. As a side…

We show that if K is a self-similar set in the plane with positive length, then the distance set of K has Hausdorff dimension one.

For any contractive iterated function system (IFS, including the Moran systems), we show that there is a natural hyperbolic graph on the symbolic space, which yields the H\"{o}lder equivalence of the hyperbolic boundary and the invariant…

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 $K$…

Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…

The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions.…

By considering a Moran-type construction of fractals on $[0,1]$, we show that for any $0\le s\le 1$, there exists some Moran fractal set, which is perfect, with Hausdorff dimension $s$ whose Fourier dimension is zero and it contains…

This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical…