Related papers: The simplest erasing substitution
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…
Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…
We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…
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…
Even though classic theories and models of discrete choice pose man as a rational being, it has been shown extensively that people persistently violate rationality in their actual choices. Recent models of decision-making take these…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
We introduce a new general framework for constructing tilings of Euclidean space, which we call multiscale substitution tilings. These tilings are generated by substitution schemes on a finite set of prototiles, in which multiple distinct…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…
In this short note, we investigate non-invertible stochastic dynamical systems on the unit interval $[0, 1]$. We provide a handy condition for unique ergodicity for systems that are injective in mean. On the other hand, we give concrete…
A procedure to obtain the symbolic dynamics for conservative dynamical systems is introduced with reference to the standard map in a strongly chaotic regime. The method extends an approach previously developed for highly dissipative…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period {\tau} . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…