Related papers: Equicontinuous delone dynamical systems
It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…
We discuss topological equicontinuity and even continuity in dynamical systems. In doing so we provide a classification of topologically transitive dynamical systems in terms of equicontinuity pairs, give a generalisation of the…
Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the extension of many standard concepts of crystallography. Here, we summarise some useful…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
In this article we construct the first examples of strongly aperiodic linearly repetitive Delone sets in non-abelian Lie groups by means of symbolic substitutions. In particular, we find such sets in all $2$-step nilpotent Lie groups with…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author recently. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations…
Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
We study relations between transitivity, mixing and periodic points on dendrites. We prove that when there is a point with dense orbit which is not an endpoint, then periodic points are dense and there is a terminal periodic decomposition…
One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on…
We show that aperiodic linearly repetitive Delone sets are densely repetitive. This confirms a conjecture of Lagarias and Pleasants.
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
In this paper, we pay attention to a weaker version of Walters's question on the existence of non-uniform cocycles for uniquely ergodic minimal dynamical systems on non-degenerate connected spaces. We will classify such dynamical systems…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
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…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
In this paper, we study the Poisson stability (in particular, stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity,…
It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…