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David Ruelle

Other affiliations: IHS Inc., Carnegie Mellon University, Rutgers University  ...read more
Bio: David Ruelle is an academic researcher from Institut des Hautes Études Scientifiques. The author has contributed to research in topics: Statistical mechanics & Dynamical systems theory. The author has an hindex of 72, co-authored 230 publications receiving 31960 citations. Previous affiliations of David Ruelle include IHS Inc. & Carnegie Mellon University.


Papers
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Book ChapterDOI
01 Jan 1995
TL;DR: In this paper, a graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples, and the tool can be used to measure the time complexity of a dynamical system.
Abstract: A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.

324 citations

Journal ArticleDOI
David Ruelle1
TL;DR: It appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general).
Abstract: We present analytic properties of the power spectrum for a class of chaotic dynamical systems (Axiom-A systems). The power spectrum is meromorphic in a strip; the position of the poles (resonances) depends on the system considered, but only their residues depend on the observable monitored. In relation with these results we also discuss the exponential or nonexponential decay of correlation functions at infinity. In conclusion, it appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general).

285 citations

Journal ArticleDOI
TL;DR: In this article, the spectral properties of transfer operators and corresponding analytic properties of the generating function are discussed, and new results are proved and some natural conjectures are proposed, and applications to Julia sets are also discussed.
Abstract: Letf:X↦X be an expanding map of a compact space (small distances are increased by a factor >1). A generating functionζ(z) is defined which countsf-periodic points with a weight. One can expressζ in terms of nonstandard “Fredholm determinants” of certain “transfer operators”, which can be studied by methods borrowed from statistical mechanics. In this paper we review the spectral properties of the transfer operators and the corresponding analytic properties ofζ(z). Gibbs distributions and applications to Julia sets are also discussed. Some new results are proved, and some natural conjectures are proposed.

282 citations

Book ChapterDOI
01 Jan 1995

260 citations

Journal ArticleDOI
TL;DR: In this paper, the large system limit of the Random Energy Model (REM) and generalized random energy model (GREM) of Derrida is investigated, and found to be universal, which permits systematic calculations of relevance to Parisi's solution of the Sherrington-Kirkpatrick spin-glass model.
Abstract: The large system limit of the Random Energy Model (REM) and generalized Random Energy Model (GREM) of Derrida is investigated, and found to be universal. This permits systematic calculations of relevance in particular to Parisi's solution of the Sherrington-Kirkpatrick spin-glass model.

236 citations


Cited by
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Book
01 Jan 1982
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

24,199 citations

Book ChapterDOI
01 Jan 1981

9,756 citations

Journal ArticleDOI
TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Abstract: Certain subsystems of nonlinear, chaotic systems can be made to synchronize by linking them with common signals. The criterion for this is the sign of the sub-Lyapunov exponents. We apply these ideas to a real set of synchronizing chaotic circuits.

9,201 citations

Journal ArticleDOI
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.

8,128 citations

Journal ArticleDOI
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

6,145 citations