Related papers: Dynamical versus diffraction spectrum for structur…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…
The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is…
The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a…
The existence of measure preserving invertible transformations $T$ with simple spectrum is established possessing the following rate of correlation decay $(f(T^k x), f(x)) = O(|k|^{-1/2+{\epsilon}})$ for a dense family of functions $f$ and…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed…
We establish connections between several properties of topological dynamical systems, such as: - every point is generic for an ergodic measure, - the map sending points to the measures they generate is continuous, - the system splits into…
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…
For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…
A dynamic diffraction theory is developed for describing electron diffraction by dielectric crystals in a strong electromagnetic field. It is shown that additional diffraction maxima arise in an electromagnetic field, their intensity…
We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We describe the spectrum of an ergodic invariant measure by examining the behaviour of its generic points. We define regular Wiener--Wintner generic points for a measure to generalise the characterisation of generic points for discrete…
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
Recently, the dynamical and spectral properties of square-free integers, visible lattice points and various generalisations have received increased attention. One reason is the connection of one-dimensional examples such as $\mathscr…
We consider the construction and classification of some new mathematical objects, called ergodic spatial stationary processes, on locally compact Abelian groups, which provide a natural and very general setting for studying diffraction and…
We present cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…