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Author:   Joachim Peinke ,  Jurgen Parisi ,  Otto E. Rossler ,  Ruedi Stoop
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.590kg
ISBN:  

9783540556473

ISBN 10:   3540556478
Pages:   299
Publication Date:   05 December 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

1 Introductory Remarks.- Problems.- 2 Semiconductor Physics.- 2.1 Fundamentals of Nonlinear Dynamics.- 2.1.1 Historical Remarks.- 2.1.2 Plasma Ansatz.- 2.1.3 Negative Differential Conductivity.- 2.1.4 Transport Mechanisms.- 2.2 Recent Experimental Progress.- 2.3 Model Experimental System.- 2.3.1 Material Characterization.- 2.3.2 Experimental Set-up.- 2.4 Experimental Results.- 2.4.1 Static Current-Voltage Characteristics.- 2.4.2 Temporal Instabilities.- 2.4.3 Spatial Structures.- 2.4.4 Spatio-Temporal Behavior.- Problems.- 3 Nonlinear Dynamics.- 3.1 Basic Ideas and Definitions.- 3.2 Fixed Points.- 3.2.1 Fundamental Bifurcations.- 3.2.2 Catastrophe Theory.- 3.2.3 Experiments.- 3.3 Periodic Oscillations.- 3.3.1 The Periodic State.- 3.3.2 Bifurcations to Periodic States.- 3.3.3 Experiments.- 3.4 Quasiperiodic Oscillations.- 3.4.1 The Quasiperiodic State.- 3.4.2 Bifurcations to Quasiperiodic States.- 3.4.3 Influence of Nonlinearities.- 3.4.4 Experiments.- 3.5 Chaotic Oscillations and Hierarchy of Dynamical States.- 3.5.1 The Chaotic State.- 3.5.2 Characterization Methods.- 3.5.3 Bifurcations to Chaotic States.- 3.6 Spatio-Temporal Dynamics.- Problems.- 4 Mathematical Background.- 4.1 Basic Concepts in the Theory of Dynamical Systems.- 4.1.1 Dissipative Dynamical Systems and Attractors.- 4.1.2 Invariant Probability Measures.- 4.1.3 Invariant Manifolds.- 4.1.4 Chaos.- 4.2 Scaling Behavior of Attractors of Dissipative Dynamical Systems.- 4.2.1 Scale Invariance.- 4.2.2 Symbolic Dynamics.- 4.2.3 Analogy with Statistical Mechanics.- 4.2.4 Partition Function for Chaotic Attractors of Dissipative Dynamical Systems.- 4.2.5 Discussion of the Partition Function.- 4.3 Generalized Dimensions, Lyapunov Exponents, Entropies.- 4.3.1 Definition of the Scaling Functions for Sampling Processes.- 4.3.2 Relation Between the Scaling Functions and a Thermodynamical Formalism.- 4.3.3 Relation Between the Scaling of the Support and the Scaling of the Measure (Generic Case).- 4.3.4 Discussion of Nonanalyticities.- 4.3.5 Evidence of Phase-Transition-Like Behavior in Experimental Observations.- 4.4 Evaluation of Experimental Systems.- 4.4.1 Embedding of a Time Series.- 4.4.2 Lyapunov Exponents from the Dynamical Equations and from Time Series.- 4.4.3 Results and Stability of Results.- 4.4.4 Comparison with Other Methods.- 4.5 High-Dimensional Systems.- 4.5.1 Singular-Value Decomposition.- 4.5.2 The Modified Approach.- 4.5.3 Results on Simulated Data.- 4.6 Lyapunov Exponents, Rotation Numbers and the Degree of Mappings.- 4.6.1 Characterization of Solutions of Dynamical Systems via the Degree of Mapping.- 4.6.2 Riemannian Motions on Manifolds of Constant Negative Curvature.- 4.7 Conclusions.- Problems.- References.

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