Related papers: Geometry of limit sets for expansive Markov system…
This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
The collective properties of small material systems considered as semidynamical systems revealing the Markov-type irreversible evolution, are investigated. It is shown that these material systems admit their treatment as thermodynamic…
We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated…
We build a Markov partition of the Feigenbaum dynamical plane, and a system of "external rays", which are invariant under rescaling. Applications to geometry of the Feigenbaum map are given.
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Using older and recent results on the integrability of two-dimensional (2d) dynamical systems, we prove that the results obtained in a recent publication concerning the 2d generalized Ermakov system can be obtained as special cases of a…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
Markov diagrams provide a way to understand the structures of topological dynamical systems. We examine the construction of such diagrams for subshifts, including some which do not have any nontrivial Markovian part, in particular Sturmian…
We give an explicit geometric description of the $\times2,\times3$ system, and use his to study a uniform family of Markov partitions related to those of Wilson and Abramov. The behaviour of these partitions is stable across expansive cones…
We introduce the notions in the title for endomorphisms of subshifts, and using them we characterize various classes of "resolving endomorphisms of subshifts" in the broad sense including onesided and weak ones. Resolving endomorphisms of…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
We give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove…