Chaos in dynamical systems. 2nd ed. (English) Zbl 1006.37001

Ott, Edward

Cambridge: Cambridge University Press (ISBN 0-521-81196-1/pbk; 0-521-01084-5/hbk). xii, 478 p. (2002).

This second edition updates and expands the first edition (see Zbl 0792.58014). A new chapter on control and synchronization of chaos is included (Chapter 10). This chapter covers such topics as control by a feedback, controlling a steadily running chaotic process, targeting, stability of chaotic set on an invariant manifold, identical, phase, and generalized synchronization of chaotic systems. Further additions concern riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos and strange nonchaotic attractors. Also, new homework problems for students have been added.
This very comprehensive book on chaotic dynamics is intended to use in a graduate course for scientists and engineers. It can also be used as a reference for researchers in the field of nonlinear dynamics.

Reviewer: Sergiy Yanchuk (Kyïv)

MSC:

37-02	Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C70	Attractors and repellers of smooth dynamical systems and their topological structure
37Cxx	Smooth dynamical systems: general theory
81Q50	Quantum chaos
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
34H05	Control problems involving ordinary differential equations

Keywords:

dynamical systems; maps; attractors; quasiperiodicity; multifractals; synchronization; control; chaos; KAM theory; Hénon; Lorenz attractors; quantum chaos