Extremes and Recurrence in Dynamical Systems

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.

305 pages book, V. Lucarini, D. Faranda, A. C. M. Freitas, J. M. Freitas, T. Kuna, M. Holland, M. Nicol, M. Todd, S. Vaienti, Extremes and Recurrence in Dynamical Systems, Wiley, New York, 2016, ISBN: 978-1-118-63219-2

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• Statistical Modeling of Spatial Extremes
• The Lyapunov Characteristic Exponents and their computation
• Stochastic Climate Theory and Modelling
• Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
• Detecting order and chaos in Hamiltonian systems by the SALI method
• Extremes and Recurrence in Dynamical Systems
• Recurrence time analysis, long-term correlations, and extreme events
• Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems
• A new framework for climate sensitivity and prediction: a modelling perspective
• A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings
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• Nonequilibrium and irreversibility
• Universal behavior of extreme value statistics for selected observables of dynamical systems
• Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach
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• From temporal to spatiotemporal dynamics in transitional plane Couette flow
• Disentangling multi-level systems: averaging, correlations and memory
• The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
• Random perturbations of non-uniformly expanding maps
• Linear response, susceptibility and resonances in chaotic toy models
• Extreme value laws in dynamical systems under physical observables
• Speed of convergence for laws of rare events and escape rates
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• Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part I: Stationary case
• Asymptotics for hitting times
• Extreme Value Statistics of the Total Energy in an Intermediate Complexity Model of the Mid-latitude Atmospheric Jet. Part II: trend detection and assessment
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• Nambu representation of an extended Lorenz model with viscous heating
• On tail trend detection: modeling relative risk
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• Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like system
• Hitting time statistics for observations of dynamical systems
• Extreme Value laws for dynamical systems under observational noise
• Predictability of threshold exceedances in dynamical systems
• Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems
• Central limit theorems for the shrinking target problem
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• Mixing properties in the advection of passive tracers via recurrences and extreme value theory
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Cited by in corpus (42)

• The Physics of Climate Variability and Climate Change
• Extremes and Recurrence in Dynamical Systems
• Extreme events in dynamical systems and random walkers: A review
• Linear response for intermittent maps
• A New Mathematical Framework for Atmospheric Blocking Events
• Distance dependent competitive interactions in a frustrated network of mobile agents
• Computing return times or return periods with rare event algorithms
• Dynamical Landscape and Multistability of a Climate Model
• Understanding the origin of extreme events in El Niño-Southern Oscillation
• Generalized dimensions, large deviations and the distribution of rare events
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Co-existing climate attractors in a coupled aquaplanet
• Scale interactions and anisotropy in stable boundary layers
• Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables
• Convergence of extreme value statistics in a two-layer quasi-geostrophic atmospheric model
• Closed-loop adaptive control of extreme events in a turbulent flow
• A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere
• Computation of extremes values of time averaged observables in climate models with large deviation techniques
• Probability distributions for analog-to-target distances
• Instabilities in quasiperiodic motion lead to intermittent large-intensity events in Zeeman laser
• New criteria to detect singularities in experimental incompressible flows
• Extreme Value Laws for dynamical systems with countable extremal sets
• Local dimension and recurrent circulation patterns in long-term climate simulations
• Shrinking targets and eventually always hitting points for interval maps
• A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization
• Extreme value distributions of observation recurrences
• Challenges and perspectives in recurrence analyses of event time series
• Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution
• Entry and return times for semi-flows
• Universal hitting time statistics for integrable flows
• Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines
• Pattern change of precipitation extremes in Bear Island
• Propagation of extreme events in multiplex neuronal networks
• Matching of observations of dynamical systems, with applications to sequence matching
• Evidence for crisis-induced intermittency during geomagnetic superchron transitions
• Inferring the instability of a dynamical system from the skill of data assimilation exercises
• Potential well in Poincaré recurrence
• Extremes for transient random walks in random sceneries under weak independence conditions
• Introduction to the Special Issue on the Statistical Mechanics of Climate
• Dimensional analysis identifies contrasting dynamics of past climate states and critical transitions
• Boosting Ensembles for Statistics of Tails at Conditionally Optimal Advance Split Times
• Stochastic and statistical stability of the classical Lorenz flow under perturbations modeling anthropogenic type forcing