Related papers: Delone sets and dynamical systems
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
The dynamics and thermodynamics of dislocated crystals are studied within the framework of the nonlinear theory of elastic and plastic deformations.
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
We introduce a new general framework for constructing tilings of Euclidean space, which we call multiscale substitution tilings. These tilings are generated by substitution schemes on a finite set of prototiles, in which multiple distinct…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
I motivate and discuss some recent work on theories with varying constants, and consider some possible observational consequences and tests. Particular emphasis is given to models which can (almost) exactly mimic the predictions of standard…
Exploration of the structure formation and dynamics of animate and inanimate matter on the nanometer scale is a highly interdisciplinary field of rapidly emerging research. It is relevant for various molecular and nanoscale systems of…
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…
We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the…
It is shown that the covering approach with a single decagonal prototile can be transformed into a hexagon, boat and star tiling. Particularly, the atomic decoration recently proposed by Cockayne and Widom (Phys. Rev. Lett. 81, 598 (1998))…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They…