Lyapunov Exponents
A Tool to Explore Complex Dynamics

A comprehensive description of the Lyapunov exponent tools from basic to advanced levels, with practical applications for complex systems.

Arkady Pikovsky (Author), Antonio Politi (Author)

9781107030428, Cambridge University Press

Hardback, published 11 February 2016

295 pages, 80 b/w illus. 3 tables
25.6 x 18.9 x 1.8 cm, 0.82 kg

'This book is written for mainly a physics audience but mathematicians may ?nd 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, Mathematical Reviews

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.

1. Introduction
2. The basics
3. Numerical methods
4. Lyapunov vectors
5. Fluctuations and generalized exponents
6. Dimensions and dynamical entropies
7. Finite amplitude exponents
8. Random systems
9. Coupled systems
10. High-dimensional systems: general
11. High-dimensional systems: Lyapunov vectors and finite-size effects
12. Applications
Appendices
Index.

Subject Areas: Physics [PH], Differential calculus & equations [PBKJ], Mathematics & science [P]