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  • Cited by 105
Publisher:
Cambridge University Press
Online publication date:
February 2016
Print publication year:
2016
Online ISBN:
9781139343473

Book description

Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.

Reviews

'… it should be required reading for anyone seriously engaged in the quantitative analysis of the dynamics of complex systems.'

Robert C. Hilborn Source: Physics Today

'This book is written for mainly a physics audience but mathematicians may find inspiration seeing how to deal with Lyapunov exponents in practice. The book gives a very comprehensive overview of the currently available tools to explore dynamical systems through the numerical study of Lyapunov exponents, Lyapunov spectra and the extraction of the corresponding Oseledets splitting. Indeed mathematical results assure the existence of exponents and the splitting for a given invariant probability measure but give few clues as to how one may compute, in particular, the splitting. This is dealt with in much detail in the book.'

Hans Henrik Rugh Source: Mathematical Reviews

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Contents

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