Related papers: The Devron property
We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at all resolutions coarser than a given…
Since seminal work of Bowen, it has been known that the specification property implies various useful properties about a topological dynamical system, among them uniqueness of the measure of maximal entropy (often referred to as intrinsic…
We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the…
We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of $V = F^{-1}(W)$ such that if $V$ has the property $A$, then $W$ must have the property $A$. We show that…
The purpose of this paper is to show that if the spectral radius of the matrix of the linearized system of a nonlinear discrete dynamical system is less then one then the characterization theorem from \cite{KBBB1,KBGB2} holds.
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the…
While quark-hadron duality is well-established experimentally, the current theoretical understanding of this important phenomenon is quite limited. To expose the essential features of the dynamics behind duality, we use a simple model in…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems.…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these…
The Poincar\'e map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincar\'e map for dynamical systems with impulse effects was…
We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
Non-linear maps can possess various dynamical behaviors varying from stable steady states and cycles to chaotic oscillations. Most models assume that individuals within a given population are identical ignoring the fundamental role of…
We consider a one-dimensional family of rational surfaces with automorphisms. In a degeneration of this family, the limiting map is the identity map on a special fiber. We check that the map on the total space of the family has…
Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…