Open AccessBook
Extremes and Recurrence in Dynamical Systems
Valerio Lucarini,Davide Faranda,Ana C. Freitas,Jorge Milhazes Freitas,Mark Holland,Tobias Kuna,Matthew Nicol,Mike Todd,Sandro Vaienti +8 more
TLDR
In this article, the authors provide a broad overview of the interdisciplinary research area of extreme events, underlining its relevance for mathematics, natural sciences, engineering, and social sciences, and discuss how extreme events can be used as probes for inferring fundamental dynamical and geometrical properties of a dynamical system.Abstract:
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its relevance for mathematics, natural sciences, engineering, and social sciences. After exploring the basics of the classical theory of extreme events, the book presents a careful examination of how a dynamical system can serve as a generator of stochastic processes, and explores in detail the relationship between the hitting and return time statistics of a dynamical system and the possibility of constructing extreme value laws for given observables. Explicit derivation of extreme value laws are then provided for selected dynamical systems. The book then discusses how extreme events can be used as probes for inferring fundamental dynamical and geometrical properties of a dynamical system and for providing a novel point of view in problems of physical and geophysical relevance. A final summary of the main results is then presented along with a discussion of open research questions. Finally, an appendix with software in Matlab programming language allows the readers to develop further understanding of the presented concepts.read more
Citations
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Dynamical proxies of North Atlantic predictability and extremes
TL;DR: Instantaneous properties of the attractor provide an efficient way of evaluating and informing operational weather forecasts and show the existence of a significant correlation between the time series of instantaneous stability and dimension and the mean spread of sea-level pressure fields in an operational ensemble weather forecast.
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Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database
TL;DR: It is found that nonparametric methods are generally not reliable, while methods that are based on GP asymptotic properties lead to unrealistically high threshold and shape parameter estimates.
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The Structure of Climate Variability Across Scales
Christian Franzke,Susana Barbosa,Richard Blender,Hege-Beate Fredriksen,Thomas Laepple,Fabrice Lambert,Tine Nilsen,Kristoffer Rypdal,Martin Rypdal,Manuel G. Scotto,Stéphane Vannitsem,Nicholas W. Watkins,Nicholas W. Watkins,Nicholas W. Watkins,Lichao Yang,Lichao Yang,Naiming Yuan +16 more
TL;DR: In this paper, the authors review various scaling mechanisms and their relevance for the climate system and discuss the application of scaling properties and methods in trend detection, climate sensitivity analyses, and climate prediction.
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Extreme Events: Mechanisms and Prediction
TL;DR: In this paper, the authors review several aspects of extreme events in phenomena described by high-dimensional, chaotic dynamical systems, focusing on two pressing aspects of the problem: (i) Mechanisms underlying the formation of Extreme Events and (ii) Real-time prediction of extreme Events.
References
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Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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Determining Lyapunov exponents from a time series
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.
The Art in Computer Programming
Andrew Hunt,Dave Thomas +1 more
TL;DR: Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.
Book
Introduction to Phase Transitions and Critical Phenomena
H. Eugene Stanley,Guenter Ahlers +1 more
TL;DR: In this article, the authors present a paperback edition of a distinguished book, originally published by Clarendon Press in 1971, which is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another.
Journal ArticleDOI
Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).