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Lai Sang Young

Bio: Lai Sang Young is an academic researcher from Courant Institute of Mathematical Sciences. The author has contributed to research in topics: Lyapunov exponent & Dynamical systems theory. The author has an hindex of 45, co-authored 140 publications receiving 9497 citations. Previous affiliations of Lai Sang Young include University of North Carolina at Chapel Hill & University of Florida.


Papers
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Journal ArticleDOI
TL;DR: In this article, the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces is discussed.
Abstract: This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors the picture has been fairly complete since the 1970’s (see [S1], [B], [R2]). Since then much progress has been made on two fronts: there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero Lyapunov exponents ([O], [P1], [Ka], [LY]), and there are detailed analyses of specific kinds of dynamical systems including, for example, billiards, 1-dimensional and Henon-type maps ([S2], [BSC]; [HK], [J]; [BC2], [BY1]). Statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero Lyapunov exponents. The goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than Axiom A. This class will not be defined explicitly, but it includes some of the much studied examples. By looking at regular returns to sets with good hyperbolic properties, one could give systems in this class a simple dynamical representation. Conditions for the existence of natural invariant measures, exponential mixing and central limit theorems are given in terms of the return times. These conditions can be checked in concrete situations, giving a unified way of proving a number of results, some new and some old. Among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of Henon-type maps.

875 citations

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TL;DR: In this paper, the authors considered the setting of a map making "nice" return to a reference set, and defined criteria for the existence of equilibria, speed of convergence to equilibrium, and central limit theorem in terms of the tail of the return time function.
Abstract: The setting of this paper consists of a map making “nice” returns to a reference set. Criteria for the existence of equilibria, speed of convergence to equilibria and for the central limit theorem are given in terms of the tail of the return time function. The abstract setting considered arises naturally in differentiable dynamical systems with some expanding or hyperbolic properties.

794 citations

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TL;DR: In this article, the authors consider diffeomorphisms of surfaces leaving invariant an ergodic Borel probability measure and define HD (μ) to be the infimum of Hausdorff dimension of sets having full μ-measure.
Abstract: We consider diffeomorphisms of surfaces leaving invariant an ergodic Borel probability measure μ. Define HD (μ) to be the infimum of Hausdorff dimension of sets having full μ-measure. We prove a formula relating HD (μ) to the entropy and Lyapunov exponents of the map. Other classical notions of fractional dimension such as capacity and Renyi dimension are discussed. They are shown to be equal to Hausdorff dimension in the present context.

634 citations

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TL;DR: In this article, a formule valable for toutes les mesures invariant to Margulis et Ruelle's inequality is defined, and demontre une formule with respect to all the invariant mesures.
Abstract: Soit M une variete de Riemann compacte, soit f:M→M un diffeomorphisme, et soit m une mesure de probabilite de Borel f-invariante sur M. On identifie les mesures pour lesquelles l'inegalite de Margulis et Ruelle qui relie l'entropie aux exposants de Lyapunov atteint l'egalite. On demontre une formule valable pour toutes les mesures invariantes

625 citations

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TL;DR: In this article, the authors reported on some of the main results surrounding an invariant measure introduced by Sinai, Ruelle, and Bowen in the 1970s, called SRB measures, as these objects are called.
Abstract: This is a slightly expanded version of the text of a lecture I gave in a conference at Rutgers University in honor of David Ruelle and Yasha Sinai. In this lecture I reported on some of the main results surrounding an invariant measure introduced by Sinai, Ruelle, and Bowen in the 1970s. SRB measures, as these objects are called, play an important role in the ergodic theory of dissipative dynamical systems with chaotic behavior. Roughly speaking,

599 citations


Cited by
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28 Jul 2005
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1(PfPMP1)与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员,通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

18,940 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
06 Jun 1986-JAMA
TL;DR: The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or her own research.
Abstract: I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

7,563 citations

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01 Dec 1992-Ecology
TL;DR: The second volume in a series on terrestrial and marine comparisons focusing on the temporal complement of the earlier spatial analysis of patchiness and pattern was published by Levin et al..
Abstract: This book is the second of two volumes in a series on terrestrial and marine comparisons, focusing on the temporal complement of the earlier spatial analysis of patchiness and pattern (Levin et al. 1993). The issue of the relationships among pattern, scale, and patchiness has been framed forcefully in John Steele’s writings of two decades (e.g., Steele 1978). There is no pattern without an observational frame. In the words of Nietzsche, “There are no facts… only interpretations.”

5,833 citations

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TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.

5,239 citations