Related papers: Model sets with Euclidean internal space
For a family of dynamical systems with $k > 0$ independent first integrals evolving in a compact region of an Euclidean space, we study the equilibrium locus. We show that under mild and generic conditions, it is a smooth manifold that can…
We call a family $\{Y_1,\dots,Y_I\}$ in Euclidean space an equidistance spacing if $\|y_i - y_j\| = 1$ whenever $y_i \in Y_i, y_j \in Y_j$ and $i \neq j$. In other words, choosing a representative from each set produces a complete distance…
We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…
We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued…
Matrix valued inner functions on the bidisk have a number of natural subspaces of the Hardy space on the torus associated to them. We study their relationship to Agler decompositions, regularity up to the boundary, and restriction maps into…
A criterion is given for a type in a finite rank stable theory to be (almost) internal to a given nonmodular minimal type. The motivation comes from results of Campana which give criteria for compact complex analytic spaces to be algebraic…
It is well known that the Fourier--Bohr coefficients of regular model sets exist and are uniformly converging, volume-averaged exponential sums. Several proofs for this statement are known, all of which use fairly abstract machinery. For…
The two-dimensional homogeneous Euclidean algorithm is the central motivation for the definition of the classical multidimensional continued fraction algorithms, as Jacobi-Perron, Poincar\'e, Brun and Selmer algorithms. The Rauzy induction,…
We show that in codimension at least 3, spaces of locally flat topological embeddings of manifolds are correctly modelled by derived spaces of maps between their configuration categories (under mild smoothability conditions). That general…
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…
We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different…
We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
Inner amenability is a bridge between amenability of an object and amenability of its operator algebras. It is an open problem of Ananantharman-Delaroche to decide whether all \'etale groupoids are inner amenable. Approximate lattices and…
Model sets are projections of certain lattice subsets. It was realised by Moody that dynamical properties of such sets are induced from the torus associated with the lattice. We follow and extend this approach by studying dynamics on the…
It is investigated a possibility of physical interpretation of vector fields (dynamic flows) in Euclidean spaces of higher dimension. There are analyzed the methods of measurements of dynamic flows, the characteristics of dynamic flow and…
Classical mechanics unfolds within absolute time and Euclidean space, yet our knowledge of where events occur, when they occur, and how motion evolves is inherently uncertain. The special Galilean group provides a natural setting for…
We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in…
We introduce a new ladder of function spaces which is shown to fill in the gap between the weak $L^{p\infty}$ spaces and the larger Morrey spaces, $M^p$. Our motivation for introducing these new spaces, denoted $\V^{pq}$, is to gain a more…
A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of $\beta \N$, or it is a "tame" topological space whose topology…