Call number:
AWI A17-94-0199
;
PIK M 410-93-0278
Description / Table of Contents:
This book is an in-depth and broad text on the subject of chaos in dynamical systems. It is intended to serve both as a graduate course text for science and engineering students, and as a reference and introduction to the subject for researchers. Within the past decades scientists, mathematicians and engineers have realized that a large variety of systems exhibit complicated evolution with time. This complicated behavior, called chaos, occurs so frequently that it has become important for the workers in many disciplines to have a good grasp of the fundamentals and basic tools of the emerging science of chaotic dynamics. Topics in the book include: attractors; basins of attraction; one-dimensional maps; fractals; natural measure; strange attractors; delay coordinate embedding; fat fractals; Hausdorff dimension; symbolic dynamics; stable and unstable manifolds; Lyapunov exponents; metric and topological entropy; controlling chaos; chaotic transients; fractal basin boundaries; chaotic scattering; quasiperiodicity; Hamiltonian systems; KAM tori; period doubling cascades; the intermittency transition to chaos; crises; bifurcations to chaos in scattering problems and in fractal basin boundaries; the characterization of dynamics by unstable periodic orbits; and quantum chaos in time-independent bounded systems, as well as in temporally kicked and scattering problems. Homework problems are also included throughout the book. - This book will be of value to advanced undergraduates and graduate students in science, engineering and mathematics taking courses in chaotic dynamics, as well as to researchers interested in the subject.
Type of Medium:
Monograph available for loan
Pages:
XII, 385 S.
Edition:
1. publ.
ISBN:
0521432154
Note:
Contents: Preface. - 1 Introduction and overview. - 1.1 Some history. - 1.2 Examples of chaotic behavior. - 1.3 Dynamical systems. - 1.4 Attractors. - 1.5 Sensitive dependence on initial conditions. - 1.6 Delay coordinates. - Problems. - Notes. - 2 One-dimensional maps. - 2.1 Piecewise linear one-dimensional maps. - 2.2 The logistic map. - 2.3 General discussion of smooth one-dimensional maps. - 2.4 Examples of applications of one-dimensional maps to chaotic systems of higher dimensionality. - Appendix: Some elementary definitions and theorems concerning sets. - Problems. - Notes. - 3 Strange attractors and fractal dimension. - 3.1 The box-counting dimension. - 3.2 The generalized baker's map. - 3.3 Measure and the spectrum of Dq dimensions. - 3.4 Dimension spectrum for the generalized baker's map. - 3.5 Character of the natural measure for the generalized baker's map. - 3.6 The pointwise dimension. - 3.7 Implications and determination of fractal dimension in experiments. - 3.8 Embedding. - 3.9 Fat fractals. - Appendix: Hausdorff dimension. - Problems. - Notes. - 4 Dynamical properties of chaotic systems. - 4.1 The horseshoe map and symbolic dynamics. - 4.2 Linear stability of steady states and periodic orbits. - 4.3 Stable and unstable manifolds. - 4.4 Lyapunov exponents. - 4.5 Entropies. - 4.6 Controlling chaos. - Appendix: Gram-Schmidt orthogonalization. - Problems. - Notes. - 5 Nonattracting chaotic sets. - 5.1 Fractal basin boundaries. - 5.2 Final state sensitivity. - 5.3 Structure of fractal basin boundaries. - 5.4 Chaotic scattering. - 5.5 The dynamics of chaotic scattering. - 5.6 The dimensions of nonattracting chaotic sets and their stable and unstable manifolds. - . - Appendix: Derivation of Eqs. (5.3). - Problems. - Notes. - 6 Quasiperiodicity. - 6.1 Frequency spectrum and attractors. - 6.2 The circle map. - 6.3 N frequency quasiperiodicity with N 〉 2. - 6.4 Strange nonchaotic attractors of quasiperiodically forced systems. - Problems. - Notes. - 7 Chaos in Hamiltonian systems. - 7.1 Hamiltonian systems. - 7.2 Perturbation of integrable systems. - 7.3 Chaos and KAM tori in systems describable by two-dimensional Hamiltonian maps. - 7.4 Higher-dimensional systems. - 7.5 Strongly chaotic systems. - 7.6 The succession of increasingly random systems. - Problems. - Notes. - 8 Chaotic transitions. - 8.1 The period doubling cascade route to chaotic attractors. - 8.2 The intermittency transition to a chaotic attractor. - 8.3 Crises. - 8.4 The Lorenz system: An example of the creation of a chaotic transient. - 8.5 Basin boundary metamorphoses. - 8.6 Bifurcations to chaotic scattering. - Problems. - Notes. - 9 Multifractals. - 9.1 The singularity spectrum f(a). - 9.2 The partition function formalism. - 9.3 Lyapunov partition functions. - 9.4 Distribution of finite time Lyapunov exponents. - 9.5 Unstable periodic orbits and the natural measure. - 9.6 Validity of the Lyapunov and periodic orbits partition functions for nonhyperbolic attractors. - Problems. - Notes. - 10 Quantum chaos. - 10.1 The energy level spectra of chaotic, bounded, time-independent systems. - 10.2 Wavefunctions for classically chaotic, bounded, time-independent systems. - 10.3 Temporally periodic systems. - 10.4 Quantum chaotic scattering. - Problems. - Notes. - References. - Index.
Location:
AWI Reading room
Location:
A 18 - must be ordered
Branch Library:
AWI Library
Branch Library:
PIK Library
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