Related papers: Dynamics measured in a non-Archimedean field
In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
We give a general method on the way of approximating equilibrium states for a dynamical system of a compact metric space.
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
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…
This survey is dedicated to a new direction in the theory of dynamical systems: the dynamics of metrics in measure spaces and new (catalytic) invariants of transformations with invariant measure. A space equipped with a measure and a metric…
Monomial mappings, $x\mapsto x^n$, are topologically transitive and ergodic with respect to Haar measure on the unit circle in the complex plane. In this paper we obtain an anologous result for monomial dynamical systems over $p-$adic…
The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions…
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…
Human communication is commonly represented as a temporal social network, and evaluated in terms of its uniqueness. We propose a set of new entropy-based measures for human communication dynamics represented within the temporal social…
We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample…
We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the…
The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum dynamics emerges and…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
Mathematical models describing the cosmological evolution of classical and phantom scalar fields with self-action are formulated and analyzed. Systems of dynamical equations in the plane, describing homogeneous cosmological models, have…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…