Related papers: A note on weak mean equicontinuity and strong mean…
We state that for continuous interval maps the existence of a non empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke,…
"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…
We study the stationary Stokes system in divergence form. The coefficients are assumed to be merely measurable in one direction and have Dini mean oscillations in the other directions. We prove that if $(u,p)$ is a weak solution of the…
Bisimulation is a concept that captures behavioural equivalence of states in a variety of types of transition systems. It has been widely studied in discrete-time settings where a key notion is the bisimulation metric which quantifies "how…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…
We prove that unique ergodicity of tensor product of $C^*$-dynamical system implies its strictly weak mixing. By means of this result a uniform weighted ergodic theorem with respect to $S$-Besicovitch sequences for strictly weak mixing…
We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a…
In this work we will focus on the existence of weak solutions for a system describing a general compressible viscous fluid in the case of the pressure being a linear function of the density and the viscous stress tensor being a non-linear…
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows…
We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…
Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…
Since seminal work of Bowen, it has been known that the specification property implies various useful properties about a topological dynamical system, among them uniqueness of the measure of maximal entropy (often referred to as intrinsic…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…