Milnor's conjecture on monotonicity of topological entropy: Results and questions

2014 ◽  
Author(s):  
Sebastian van Strien
Keyword(s):  
Topological Entropy ◽  
State Of The Art ◽  
Rigidity Theorem ◽  
Real Polynomial ◽  
Open Problems ◽  
Polynomial Maps ◽  
History Of ◽  
The Subject ◽  
Quadratic Case ◽  
Real Polynomial Maps

This chapter discusses Milnor's conjecture on monotonicity of entropy and gives a short exposition of the ideas used in its proof. It discusses the history of this conjecture, gives an outline of the proof in the general case, and describes the state of the art in the subject. The proof makes use of an important result by Kozlovski, Shen, and van Strien on the density of hyperbolicity in the space of real polynomial maps, which is a far-reaching generalization of the Thurston Rigidity Theorem. (In the quadratic case, density of hyperbolicity had been proved in studies done by M. Lyubich and J. Graczyk and G. Swiatek.) The chapter concludes with a list of open problems.

History of Mathematics in the Islamic World: The Present State of the Art

1985 ◽  
Vol 19 (1) ◽  
pp. 9-33 ◽  
Author(s):  
J. L. Berggren
Keyword(s):  
Present State ◽  
State Of The Art ◽  
History Of Mathematics ◽  
Islamic Culture ◽  
Islamic World ◽  
History Of ◽  
The Subject ◽  
Mathematical Sciences ◽  
Islamic Mathematics

In Recent Years, many discoveries in the history of Islamic mathematics have not been reported outside the specialist literature, even though they raise issues of interest to a larger audience. Thus, our aim in writing this survey is to provide to scholars of Islamic culture an account of the major themes and discoveries of the last decade of research on the history of mathematics in the Islamic world. However, the subject of mathematics comprised much more than what a modern mathematician might think of as belonging to mathematics, so our survey is an overview of what may best be called the “mathematical sciences” in Islam; that is, in addition to such topics as arithmetic, algebra, and geometry we will also be interested in mechanics, optics, and mathematical instruments.

scholarly journals Real Polynomial Maps and Singular Open Books at Infinity

2016 ◽  
Vol 118 (1) ◽  
pp. 57 ◽  
Author(s):  
Raimundo N. Araújo Dos Santos ◽  
Ying Chen ◽  
Mihai Tibăr
Keyword(s):  
Open Book ◽  
Real Polynomial ◽  
Open Books ◽  
Polynomial Maps ◽  
Real Polynomial Maps

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S^{m-1}_R$ of large enough radius $R$. We obtain new classes of real polynomial maps $\mathsf{R}^m \to \mathsf{R}^p$ which induce such structures.

scholarly journals A Survey of the Elastic Flow of Curves and Networks

2021 ◽  
Author(s):  
Carlo Mantegazza ◽  
Alessandra Pluda ◽  
Marco Pozzetta
Keyword(s):  
Global Existence ◽  
Critical Points ◽  
State Of The Art ◽  
The State ◽  
Open Problems ◽  
Complete Proof ◽  
Closed Curves ◽  
Smooth Convergence ◽  
The Subject

AbstractWe collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in $${\mathbb {R}}^2$$ R 2 . In the last section of the paper we also discuss a list of open problems.

scholarly journals On the Euler characteristic of fibres of real polynomial maps

1998 ◽  
Vol 44 (1) ◽  
pp. 175-182 ◽  
Author(s):  
Adam Parusiński ◽  
Zbigniew Szafraniec
Keyword(s):  
Euler Characteristic ◽  
Real Polynomial ◽  
Polynomial Maps ◽  
Real Polynomial Maps

scholarly journals On open real polynomial maps

1996 ◽  
Vol 110 (3) ◽  
pp. 297-304 ◽  
Author(s):  
J.M. Gamboa ◽  
F. Ronga
Keyword(s):  
Real Polynomial ◽  
Polynomial Maps ◽  
Real Polynomial Maps

scholarly journals Ble Based Indoor Positioning System and Minimal Zone Searching Algorithm (MZS) Applied to Visitor Trajectories within a Museum

2021 ◽  
Vol 11 (13) ◽  
pp. 6107
Author(s):  
Richard Jérémy ◽  
Bertet Karell ◽  
Faucher Cyril
Keyword(s):  
High School ◽  
Indoor Localization ◽  
State Of The Art ◽  
Indoor Positioning ◽  
Positioning System ◽  
Average Surface ◽  
The Public ◽  
History Of ◽  
The Subject ◽  
Indoor Positioning System

Museums are perfect experimentation grounds for indoor positioning technologies. Indeed, museum managers are always pleased to hold these kinds of events where it offers the opportunity to the public to be a part of such experimentation and allowing us at the same time to popularize our research with them. In this paper, we describe an experiment that held within the museum of natural history of La Rochelle with a class of high school volunteers. We will explain our systems that has been built to work in this specific case, and among other things formalize our algorithm for indoor localization that has not had an equivalent in the state of the art. The minimal zone searching algorithm (MZS) can compute in real time the position of a visitor, shaped as a zone with an average surface of 3 m2 when resources are limited and when the placement of nodes must respect the constraints imposed by the room’s layout. This method offered good results with data collected during the experimentation, such as a meaningful representation of the position of a visitor and most importantly a stable execution during the whole experience even when the subject was in tight spaces.

CONJECTURES ABOUT SIMPLE DYNAMICS FOR SOME REAL NEWTON MAPS ON ℝ2

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950099 ◽  
Author(s):  
ROBERTO DE LEO
Keyword(s):  
Julia Set ◽  
Rational Functions ◽  
Real Polynomial ◽  
One Dimensional ◽  
Polynomial Maps ◽  
Open Set ◽  
Complex Roots ◽  
Wandering Domain ◽  
Set Of Points ◽  
Real Polynomial Maps

We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, in one variable and we provide numerical evidence that the dynamics of Newton maps [Formula: see text] associated to real polynomial maps [Formula: see text] with no complex roots has a complexity comparable with that of complex Newton maps in one variable. In particular such a map [Formula: see text] has no wandering domain, almost every point under [Formula: see text] is asymptotic to a fixed point and there is some non-empty open set of points whose [Formula: see text]-limit equals the set of non-regular points of the Julia set of [Formula: see text]. The first two points were proved by B. Barna in the real one-dimensional case.

scholarly journals Toward Effective Detection of the Bifurcation Locus of Real Polynomial Maps

2016 ◽  
Vol 17 (3) ◽  
pp. 837-849 ◽  
Author(s):  
Luis Renato G. Dias ◽  
Susumu Tanabé ◽  
Mihai Tibăr
Keyword(s):  
Real Polynomial ◽  
Bifurcation Locus ◽  
Polynomial Maps ◽  
Real Polynomial Maps

A review of experimental techniques to predict aircraft spin and recovery characteristics

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bilal Malik ◽  
Jehanzeb Masud ◽  
Suhail Akhtar
Keyword(s):  
Design Methodology ◽  
State Of The Art ◽  
Experimental Techniques ◽  
Dynamic Force ◽  
Free Flight ◽  
Open Problems ◽  
Flight Tests ◽  
Content Type ◽  
Novel Technique ◽  
The Subject

Purpose This paper aims to provide a detailed review of the experimental research on the prediction of aircraft spin and recovery characteristics using dynamically scaled aircraft models. Design/methodology/approach The paper organizes experimental techniques to predict aircraft spin and recovery characteristics into three broad categories: dynamic free-flight tests, dynamic force tests and a relatively novel technique called wind tunnel based virtual flight testing. Findings After a thorough review, usefulness, limitations and open problems in the presented techniques are highlighted to provide a useful reference to researchers. The area of application of each technique within the research scope of aircraft spin is also presented. Originality/value Previous reviews on the prediction of aircraft spin and recovery characteristics were published many years ago and also have confined scope as they address particular spin technologies. This paper attempts to provide a comprehensive review on the subject and fill the information void regarding the state of the art aircraft spin technologies.

Sign in / Sign up

Export Citation Format

Share Document