Related papers: Dimension Groups and Dynamical Systems
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
Here the Integral Value Transformations (IVTs) are considered to be Discrete Dynamical System map in the space\mathbb{N}_(0). In this paper, the dynamics of IVTs is deciphered through the light of Topological Dynamics.
We discuss $\mathcal{D}$-modules and dynamical systems in the \'etale topology. We introduce the differential scheme associated to a morphism $f: X\to S$ of schemes of the same dimension. We introduce differential inertia group $I_{diff}^i$…
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
For minimal $\mathbb{Z}^{2}$-topological dynamical systems, we introduce a cube structure and a variation of the regionally proximal relation for $\mathbb{Z}^2$ actions, which allow us to characterize product systems and their factors. We…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
We investigate the category of discrete topological spaces, with emphasis on inverse systems of height $\omega_1$. Their inverse limits belong to the class of $P$-spaces, which allows us to explore dimensional types of these spaces.
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and…
In this paper, we pay attention to a weaker version of Walters's question on the existence of non-uniform cocycles for uniquely ergodic minimal dynamical systems on non-degenerate connected spaces. We will classify such dynamical systems…