Related papers: Eventual nonsensitivity and tame dynamical systems
We numerically exhibit strange scaling and temporal evolution of finite-size fluctuation in thermal equilibrium of a simple long-range interacting system. These phenomena are explained from the view point of existence of the Casimirs and…
We show that an $R^d$-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is $\mu$-mean equicontinuous (proven for $Z^d$ before). In order to do this we introduce mean equicontinuity…
We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
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 limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and…
Recently it has been shown that interparticle interactions\emph ongenerically\emph default destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this work we rigorously construct a…
In this paper, we study the dynamics of a non-autonomous dynamical system $(X,\mathbb{F})$ generated by a sequence $(f_n)$ of continuous self maps converging uniformly to $f$. We relate the dynamics of the non-autonomous system…
We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations.…
For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity…
Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is…
A big-isotropic structure $E$ is an isotropic subbundle of $TM\oplus T^*M$, endowed with the metric defined by pairing. The structure $E$ is said to be integrable if the Courant bracket $[\mathcal{X},\mathcal{Y}]\in\Gamma E$,…
We are interested in the asymptotic behaviour of the first return time of the orbits of a dynamical system into a small neighbourhood of their starting points. We study this quantity in the context of dynamical systems preserving an…
We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…
Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly…
In this paper, we introduce generalized dichotomies for nonautonomous random linear dynamical systems acting on arbitrary Banach spaces, and obtain their complete characterization in terms of an appropriate admissibility property. These…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…