Lyapunov Exponents: A Tool to Explore Complex Dynamics

ISBN-13: 9781107030428 / Angielski / Twarda / 2016 / 295 str.

Arkady Pikovsky; Antonio Politi

Opis

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

Recenzje

'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, Mathematical Reviews

Spis treści

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.