Arkady Pikovsky's Books

Strange Nonchaotic Attractors

Dynamics Between Order and Chaos in Quasiperiodically Forced Systems

By: Ulrike Feudel,Sergey Kuznetsov,Arkady Pikovsky

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Strange Nonchaotic Attractors

Dynamics Between Order and Chaos in Quasiperiodically Forced Systems

By: Ulrike Feudel,Sergey Kuznetsov,Arkady Pikovsky

This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed. Key Features Topics are suitable for various disciplines dealing with nonlinear dynamics (mechanics, physics, nonlinear optics, hydrodynamics, chemical kinetics, etc.) A variety of theoretical tools is supplied to reveal different characteristics of strange nonchaotic behavior Readership: Graduate students and researchers in nonlinear science.

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Page Count

226

Publisher

World Scientific

Published Date

ISBN 10

9812566333

ISBN 13

9789812566331

Lyapunov Exponents

A Tool to Explore Complex Dynamics

By: Arkady Pikovsky,Antonio Politi

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Lyapunov Exponents

A Tool to Explore Complex Dynamics

By: Arkady Pikovsky,Antonio Politi

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.

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