Related papers: Effective dynamical systems beyond dimension zero …
We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero modes should be handled in…
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
We consider topological dynamical systems $(X,T)$, where $X$ is a compact metrizable space and $T$ denotes an action of a countable amenable group $G$ on $X$ by homeomorphisms. For two such systems $(X,T)$ and $(Y,S)$ and a factor map $\pi…
Active matter consumes energy from the environment and transforms it into mechanical work. Notable examples from biology include cell division, bacterial swarms, and muscle contraction. In this work, we investigate the nature of active…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total,…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
We investigate projections to odometers (group rotations over adic groups) of topological invertible dynamical systems with discrete time and compact Hausdorff phase space. For a dynamical system $(X, f)$ with a compact phase space we…
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
Complex and even chaotic dynamics, though prevalent in many natural and engineered systems, has been largely avoided in the design of electromechanical systems due to concerns about wear and controlability. Here, we demonstrate that complex…
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^r$ open sets ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting…
We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. We show that there exists an effective transfer matrix labeled by the scale factor which properly describes the evolution of the quantum universe. In…
We show that every effectively closed action of a finitely generated group $G$ on a closed subset of $\{0,1\}^{\mathbb{N}}$ can be obtained as a topological factor of the $G$-subaction of a $(G \times H_1 \times H_2)$-subshift of finite…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
This paper introduces effectful toposes as an extension of the effective topos and investigates their structure relative to Lawvere-Tierney topologies. First, we formulate effectful toposes by lifting the evidenced frame, which is a…
In this article, we establish the foundations of a computational field theory, which we term Topological Kleene Field Theory (TKFT), inspired by Stephen Kleene's seminal work on partial recursive functions and drawing parallels with…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…