Related papers: Image sets in measurable dynamics

We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…

Can we learn the physics of matter in motion directly from images and video--and trust it? Answering this question requires integrating experiments, physics-based simulation, and data across traditionally separate disciplines. Much of this…

We establish connections between several properties of topological dynamical systems, such as: - every point is generic for an ergodic measure, - the map sending points to the measures they generate is continuous, - the system splits into…

This note generalizes Berge's maximum theorem to noncompact image sets. It is also clarifies the results from E.A. Feinberg, P.O. Kasyanov, N.V. Zadoianchuk, "Berge's theorem for noncompact image sets," J. Math. Anal. Appl. 397(1)(2013),…

In this article we show that a large class of infinite measure preserving dynamical systems that do not admit physical measures nevertheless exhibit strong statistical properties. In particular, we give sufficient conditions for existence…

We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly…

Systems of germs of sets in infinite-dimensional spaces are introduced and studied. Such a system corresponds to a local zero-set of an ideal of the ring of analytic functions of infinite number of variables. Conversely, this system of…

We introduce two abstract constructions for building new measurable dynamical systems from existing ones and study their ergodic properties. The first of these constructions, a "reciprocal transformation," produces a type of non-singular…

We present recent results about the asymptotic behavior of ergodic products of isometries of a metric space X. If we assume that the displacement is integrable, then either there is a sublinear diffusion or there is, for almost every…

Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…

Metrizable spaces are studied in which every closed set is an $\alpha$-limit set for some continuous map and some point. It is shown that this property is enjoyed by every space containing sufficiently many arcs (formalized in the notion of…

In a real-world setting, visual recognition systems can be brought to make predictions for images belonging to previously unknown class labels. In order to make semantically meaningful predictions for such inputs, we propose a two-step…

Most image-to-image translation models postulate that a unique correspondence exists between the semantic classes of the source and target domains. However, this assumption does not always hold in real-world scenarios due to divergent…

This paper is aim to extend Kenneth R. Berg's findings on the maximal entropy theorem and the ergodicity of measure convolution to the case of surjective homomorphisms. We further explores dynamical systems under surjective homomorphism in…

For every positive integer $n\geq 2$, we introduce the concept of measure-theoretic $n$-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically…

The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…

We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of…

We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.

For a given ergodic measure preserving transformation T of a standard measure space each finite labelled partition defines an ergodic stationary process. There is a complete metric on the space of partitions which is separable. Various…

These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…