Related papers: Indefinite Descriptive Proximities Inherent in Dyn…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We will consider various definitions of topological entropy for multivalued nonautonomous dynamical systems in compact Hausdorff spaces. Some of them can deal with arbitrary multivalued maps, i.e. when no restrictions are imposed on them.…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
We define coarse proximity structures, which are an analog of small-scale proximity spaces in the large-scale context. We show that metric spaces induce coarse proximity structures, and we construct a natural small-scale proximity…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
We introduce a novel quantity for general dynamical systems, which we call the asymptotic uniform complexity. We prove an inequality relating the asymptotic uniform complexity of a dynamical system to its mean topological matching number.…
We consider a dynamical system which has the hyperbolic structure along an attracting invariant manifold $M$. The problem is whether every motion starting in a neighborhood of $M$ possesses an asymptotic phase, i.e. eventually approaches a…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
Contrary to the established view of the Lorenz system as an archetype of dissipative chaos lacking conserved quantities, this work rigorously demonstrates the existence of a novel class of history-dependent dynamical invariants. Through a…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…