Related papers: Image sets in measurable dynamics
We call a dynamical system on a measurable metric space {\em measure-expansive} if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces…
We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into…
This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to…
CycleGAN provides a framework to train image-to-image translation with unpaired datasets using cycle consistency loss [4]. While results are great in many applications, the pixel level cycle consistency can potentially be problematic and…
The automaton transformation of infinite words over alphabet $\mathbb F_p=\{0,1,\ldots,p-1\}$, where $p$ is a prime number, coincide with the continuous transformation (with respect to the $p$-adic metric) of a ring $\mathbb Z_p$ of…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
In a series of papers, M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the…
The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not…
Transmission imaging, as an important imaging technique widely used in astronomy, medical diagnosis, and biology science, has been shown in [49] quite different from reflection imaging used in our everyday life. Understanding the structures…
Our goal is to present the basic results on one-dimensional Gibbs and equilibrium states viewed as special invariant measures on symbolic dynamical systems, and then to describe without technicalities a sample of results they allowed to…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
In this work the problem about an existence of non-measurable automorphisms of Lie groups finite and as well infinite dimensional over the field of real numbers and also over the non-archimedean local fields is investigated.…
It is shown how to model any automorphism of a totally disconnected, locally compact group by a symbolic dynamical system. The model is an inverse limit of a product of a full-shift, on a finite number of symbols, with one of two types of…
In this article we will investigate nonmeasurability with respect to some $\sigma$-ideals in Polish space $X,$ of images of subsets of $X$ by selected mappings defined on the space $X$. Among of them we answer the following question: "It is…
For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…
We study the invariant measures of typical $C^0$ maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak$^*$ closure of the set of ergodic measurescoincides with the weak$^*$…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…