A. J. Lichtenberg, M. A. Lieberman (auth.)9780387977454, 0387977457
Regular and Chaotic Dynamics treats chaotic motion in nonlinear dynamical systems. It describes a rapidly growing field with applications throughout science and engineering. The main emphasis of the first edition was on intrinsic stochasticity in Hamiltonian systems. This has been broadened to include a thorough introduction to chaotic motion in dissipative systems in the final two chapters. Our treatment emphasizes physical insight rather than mathematical rigor. We present practical methods for describing the dynamics, for determining transitions from regular to stochastic behavior and routes to chaos, and for characterizing Hamiltonian chaos and dissipative chaotic attractors. We rely heavily on numerical computations to illustrate the methods and to validate them. The book is intended to be used as a self-contained text for physical scientists and engineers who wish to enter the field, as a reference for those researchers familiar with the methods, and as an advanced graduate textbook in dynamics. |
Table of contents :
Front Matter….Pages i-xxi
Overview and Basic Concepts….Pages 1-62
Canonical Perturbation Theory….Pages 63-149
Mappings and Linear Stability….Pages 150-212
Transition to Global Stochasticity….Pages 213-258
Stochastic Motion and Diffusion….Pages 259-308
Three or More Degrees of Freedom….Pages 309-379
Dissipative Systems….Pages 380-452
Back Matter….Pages 453-499 |
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