Related papers: Coding map for a contractive Markov system

Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.

We introduce "logically contractive mappings" nonexpansive self-maps that contract along a subsequence of iterates and prove a fixed-point theorem that extends Banach's principle. We obtain event-indexed convergence rates and, under bounded…

A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

A technique of dynamically defined measures is developed and its relation to the theory of equilibrium states is shown. The technique uses Caratheodory's method and the outer measure introduced in (I. Werner, Math. Proc. Camb. Phil. Soc.…

The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate.…

A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.

Olatinwo [3] introduced contractive definitions of the derivative type, and gave a new characterization of the Banach contraction principle, and fixed point theorems for contractions defined implicitly. On the other hand Ampadu et.al [4]…

We introduce a variant of stable logarithmic maps, which we call punctured logarithmic maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points have a negative order of tangency with boundary divisors. As a…

We continue the study of Markov systems started in \cite{Wer1}. In this paper, we prove a generalization of Breiman's strong low of large numbers \cite{Br} which implies a necessary condition for the uniqueness of the stationary state of a…

We prove that a topologically generic network (an open and dense set of networks) of three or more inhibitory neurons have periodic behavior with a finite number of limit cycles that persist under small perturbations of the structure of the…

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic…

We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of \(\bR^d\). We prove that generically the attractor and the set of discontinuities of such a map are disjoint, and hence the…

This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…

We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…

This is the fifth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part V), we study products and iterates…

Weight systems are functions on chord diagrams satisfying Vassiliev's $4$-term relations. They originate in the theory of finite type knot invariants. Recent developments in understanding weight systems arising from Lie algebras are based…

This paper reviews the description of "bar codes" for a continuous real-valued map and explains how to recover the Morse complex of a Morse function from them. In this presentation the bar codes appear as the support of two vector-space…

Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…