Related papers: Dynamics on dendrites with closed endpoint sets
We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at…
In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a…
We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
This paper establishes some criteria of chaos in non-autonomous discrete systems. Several criteria of strong Li-Yorke chaos are given. Based on these results, some criteria of distributional chaos in a sequence are established. Moreover,…
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's continua. Certain theorems on dimension-lowering maps are proved for…
Aiming at a better understanding of finite groups as finite dynamical systems, we show that by a version of Fitting's Lemma for groups, each state space of an endomorphism of a finite group is a graph tensor product of a finite directed…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
If a topological dynamical system $(X,T)$ has positive topological entropy, then it is multivariant mean Li-Yorke chaotic along a sequence $\{a_k\}_{k=1}^\infty$ of positive integers which is "good" for pointwise ergodic convergence with a…
In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the dynamics is shown to be Devaney and Li-Yorke chaotic. It…
We study the structure of the branch set of solutions to Plateau's problem in metric spaces satisfying a quadratic isoperimetric inequality. In our first result, we give examples of spaces with isoperimetric constant arbitrarily close to…
Complex 1-variable polynomials with connected Julia sets and only repelling periodic points are called \emph{dendritic}. By results of Kiwi, any dendritic polynomial is semi-conjugate to a topological polynomial whose topological Julia set…
We study direct and inverse scattering problem for systems of interacting particles, having web-like structure. Such systems consist of a finite number of semi-infinite chains attached to the central part formed by a finite number of…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…
In this paper, we study geometric features of orientation-preserving random dynamical systems on the circle driven by memoryless noise that exhibit stable synchronisation: we consider crack points, invariant measures, and the link between…
We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…