Showing papers by "David Ruelle published in 1994"
Book•
01 Apr 1994
144 citations
TL;DR: The success of the ideas of chaos has led to attempts to apply them to a great variety of situations as mentioned in this paper, but the results are not always up to expectations, and in some cases the result is predictably of little interest.
Abstract: The success of the ideas of chaos has led to attempts to apply them to a great variety of situations. This is in principle a good strategy, but the results are not always up to expectations. In some cases the results are predictably of little interest. Suppose you have concocted a mathematical model in biology or economics; you put this model on your computer and you discover a Feigenbaum period‐doubling cascade, which is often a sign that chaos is present. Is this result interesting? Well, probably not. One reason is that the detailed dynamical properties of your model may not have anything to do with the properties of the real‐life system. Another reason why your discovery may be without interest is that the occurrence of a Feigenbaum cascade need not have any particular biological or economic significance: You still have to address the problem of the relevance of your finding for biology or economics.
110 citations
61 citations
TL;DR: In this article, a weighted kneading matrix which generalizes the Milnor-Thurston matrix was proposed. But the determinant of this matrix is related to a natural weighted zeta function.
Abstract: We consider a piecewise continuous, piecewise monotone interval map and a piecewise constant weight. With these data we associate a weighted kneading matrix which generalizes the Milnor—Thurston matrix. We show that the determinant of this matrix is related to a natural weighted zeta function.
51 citations
45 citations
Book•
[...]
01 Aug 1994
TL;DR: In this article, Zufall et al. discuss the empfindliche abhangigkeit von den Anfangsbedingungen. And they discuss the wahre Bedeutung von Sex.
Abstract: 1 Zufall.- 2 Mathematik und Physik.- 3 Wahrscheinlichkeiten-. 4 Lotterie und Horoskop.- 5 Klassischer Determinismus.- 6 Spiele.- 7 Die empfindliche Abhangigkeit von den Anfangsbedingungen.- 8 Hadamard, Duhem und Poincare.- 9 Turbulenz: Moden.- 10 Turbulenz: seltsame Attraktoren.- 11 Chaos: ein neues Paradigma.- 12 Chaos: Folgerungen.- 13 Okonomie.- 14 Geschichtliche Entwicklungen.- 15 Quanten: der begriffliche Rahmen.- 16 Quanten: Zahlen von Zustanden.- 17 Entropie.- 18 Irreversibilitat.- 19 Statistische Mechanik des Gleichgewichts.- 20 Siedendes Wasser und die Tore zur Holle.- 21 Information.- 22 Algorithmische Komplexitat.- 23 Komplexitat und Godels Theorem.- 24 Die wahre Bedeutung von Sex.- 25 Intelligenz.- 26 Epilog: Wissenschaft.- Anmerkungen.-
25 citations
TL;DR: In this article, a dynamical zeta function and a transfer operator are associated with a piecewise monotone map and a weight function, and the analytic properties of the spectral properties are related by a theorem of Baladi and Keller under an assumption of ''generating partition''.
Abstract: A dynamical zeta function $\zeta$ and a transfer operator $\scr L$ are associated with a piecewise monotone map $f$ of the interval $[0,1]$ and a weight function $g$. The analytic properties of $\zeta$ and the spectral properties of $\scr L$ are related by a theorem of Baladi and Keller under an assumption of ``generating partition''. It is shown here how to remove this assumption and, in particular, extend the theorem of Baladi and Keller to the case when $f$ has negative Schwarzian derivative.
13 citations
Posted Content•
TL;DR: In this paper, the role of rigor in mathematics and the relation between mathematics and theoretical physics is discussed in a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn.
Abstract: This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between mathematics and theoretical physics.
3 citations
TL;DR: In this way, reputable scientists have expressed their ideas on the irreversibility of time and Roger Penrose his own special views on consciousness and the collapse of wave packets as mentioned in this paper.
Abstract: Time and time again reputable scientists have disagreed with some part of accepted scientific doctrine. And one thing they can then do is write a book for the general public, letting us have a piece of their minds. In this way Ilya Prigogine has expressed his ideas on the irreversibility of time and Roger Penrose his own special views on consciousness and the collapse of wave packets.
1 citations
Posted Content•
TL;DR: In this paper, a dynamical zeta function and a transfer operator are associated with a piecewise monotone map and a weight function, and the analytic properties of the spectral properties are related by a theorem of Baladi and Keller under an assumption of ''generating partition''.
Abstract: A dynamical zeta function $\zeta$ and a transfer operator $\scr L$ are associated with a piecewise monotone map $f$ of the interval $[0,1]$ and a weight function $g$. The analytic properties of $\zeta$ and the spectral properties of $\scr L$ are related by a theorem of Baladi and Keller under an assumption of ``generating partition''. It is shown here how to remove this assumption and, in particular, extend the theorem of Baladi and Keller to the case when $f$ has negative Schwarzian derivative.