𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Chaotic Properties of Mappings on a Probability Space

✍ Scribed by Christophe Abraham; Gérard Biau; Benoı̂t Cadre

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
111 KB
Volume
266
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. We first give sufficient conditions (both topological and ergodic) on an endomorphism to ensure the sensitivity property. Then, a strong sensitivity concept is introduced. Sufficient conditions on a transformation implying strong sensitivity are given. We also provide bounds for the strong sensitivity constant.  2002 Elsevier Science (USA)

📜 SIMILAR VOLUMES

A Chaotic Continuous Map Generates All P
A Chaotic Continuous Map Generates All Probability Distributions
✍ F. Balibrea; J. Smital 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 439 KB

Let \(f\) be a continuous map of the compact unit interval \(l=[0,1]\), such that \(f^{2}\), the second iterate of \(f\), is topologically transitive in \(I\). If for some \(x\) and \(y\) in \(I\) and any \(t\) in \(I\) there exists \(\lim (1 / n) \#\left\{i \leqslant n ;\left|f^{i}(x)-f^{i}(y)\righ

Concentration Property on Probability Sp
Concentration Property on Probability Spaces
✍ A.A. Giannopoulos; V.D. Milman 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 226 KB

## Introduction 1.1. The starting point of this paper is the notion of concentration for metric probability spaces. Let (X, d, +) be a metric space with metric d and diameter diam(X) 1, which is also equipped with a Borel probability measure +. We then define the concentration function (or ``isoper

Contraction Type Mappings on a 2-Metric
Contraction Type Mappings on a 2-Metric Space
✍ B. E. Rhoades 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 235 KB

The concept of a 2-metric space hw been investigated by 5. G~ELER in a seriea of papers [6]-[S]. Other papers dealing with 2-metric spaces are [3]-[S], [lo], and [ 123. In this note several fixed point theorems a m proved for contractive mappings in a 2-metric space. The contradive definitions used

The bounded approximation property for s
The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces
✍ Erhan Çalışkan 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 175 KB 👁 1 views

## Abstract We study the bounded approximation property for spaces of holomorphic functions. We show that if __U__ is a balanced open subset of a Fréchet–Schwartz space or (__DFM__ )‐space __E__ , then the space ℋ︁(__U__ ) of holomorphic mappings on __U__ , with the compact‐open topology, has the b