Preface |
Prologue: Science in an Age of Transition |
Complexity In Nature / 1: |
What is complexity? / 1.1: |
Self-organization in physico-chemical systems: the birth of complexity / 1.2: |
Thermal convection, a prototype of self-organization phenomena in physics / 1.3: |
Self-organization phenomena in chemistry / 1.4: |
Physico-chemical complexity and algorithmic complexity / 1.5: |
Some further examples of complex behavior on our scale / 1.6: |
Again, biological systems / 1.7: |
Complexity at the planetary and the cosmic scale / 1.8: |
Forces versus correlations--a summing up / 1.9: |
The Vocabulary Of Complexity / 2: |
Conservative systems / 2.1: |
Dissipative systems / 2.2: |
Mechanical and thermodynamic equilibrium. Nonequilibrium constraints / 2.3: |
Nonlinearity and feedbacks / 2.4: |
The many facets of the second law / 2.5: |
Stability / 2.6: |
Bifuraction and symmetry breaking / 2.7: |
Order and correlations / 2.8: |
Dynamical Systems And Complexity / 3: |
The geometry of phase space / 3.1: |
Measures in phase space / 3.2: |
Integrable conservative systems / 3.3: |
Bifurcation in simple dissipative systems: search for archetypes of complexity / 3.4: |
Dissipative systems in two-dimensional phase spaces: limit cycles / 3.5: |
Reduction to low-dimensional systems: order parameters and normal forms / 3.6: |
Phase space revisited: topological manifolds and fractals / 3.7: |
Nonintegrable conservative systems: the new mechanics / 3.8: |
A model of unstable motion: the horseshoe / 3.9: |
Dissipative systems in multidimensional phase spaces. Chaos and strange attractors / 3.10: |
Spatially distributed systems. Symmetry-breaking bifurcations and morphogenesis / 3.11: |
Discrete dynamical systems. Cellular automata / 3.12: |
Asymmetry, selection, and information / 3.13: |
Randomness And Complexity / 4: |
Fluctuations and probabilistic description / 4.1: |
Markov processes. Master equation / 4.2: |
Markov processes and irreversibility. Information entropy and physical entropy / 4.3: |
Spatial correlations and critical behavior / 4.4: |
Time-dependent behavior of the fluctuations. The kinetics and the time scales of self-organization / 4.5: |
Sensitivity and selection / 4.6: |
Symbolic dynamics and information / 4.7: |
Generation of asymmetric, information-rich structures / 4.8: |
Once again, algorithmic complexity / 4.9: |
Toward A Unified Formulation Of Complexity / 5: |
General properties of conserved dynamical systems / 5.1: |
General properties of dissipative dynamical systems / 5.2: |
The search for unification / 5.3: |
Probability and dynamics / 5.4: |
The Baker transformation / 5.5: |
Manifolds with broken time symmetry / 5.6: |
The symmetry-breaking transformation [Lambda] / 5.7: |
Gibbs ensembles and Boltzmann ensembles / 5.8: |
Kinetic theory / 5.9: |
Resonance and light-matter interaction / 5.10: |
Concluding remarks / 5.11: |
Complexity And The Transfer Of Knowledge / 6: |
Nonlinear dynamics in far-from-equilibrium conditions and the modeling of complexity / 6.1: |
Materials science / 6.2: |
Threshold phenomena in cellular dynamics / 6.3: |
Modeling climatic change and variability / 6.4: |
Probabilistic behavior and adaptive strategies in social insects / 6.5: |
Self-organization in human systems / 6.6: |
Linear Stability Analysis / Appendix 1: |
Basic equations / A1.1: |
The principle of linearized stability / A1.2: |
The characteristic equation / A1.3: |
Illustrations / A1.4: |
Systems exhibiting chaotic dynamics / A1.5: |
Bifurcation Analysis / Appendix 2: |
General properties / A2.1: |
Expansion of the solution in perturbation series / A2.2: |
The bifurcation equations / A2.3: |
Perturbation Of Resonant Motions In Nonintegrable Conservative Systems / Appendix 3: |
The twist map / A3.1: |
Effect of the perturbation in the case of rational rotation numbers / A3.2: |
Homoclinic points / A3.3: |
Reconstruction Of The Dynamics Of Complex Systems From Time Series Data. Application To Climatic Variability / Appendix 4: |
Introductory comments / A4.1: |
Theoretical background for data analysis / A4.2: |
The climatic attractor / A4.3: |
Conclusion and perspectives / A4.4: |
Primordial Irreversible Processes / Appendix 5: |
Introduction / A5.1: |
Standard cosmological model / A5.2: |
Black holes / A5.3: |
The role of irreversibility / A5.4: |
Suggestions for Further Reading |
Index |
Preface |
Prologue: Science in an Age of Transition |
Complexity In Nature / 1: |