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Nonlinear science /
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Washington, D.C. :
National Academy Press,
1997.
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| Colección: | Compass series (Washington, D.C.)
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro
- Preface
- Contents
- 1 What Is NONLINEAR?
- Nature and Science
- Natura Vexata
- Syndrome
- Déconstruction of Linear Theory
- The Scale of Phenomenon / Theory with Scale
- The Role of Scale in Scientific Revolutions
- The Mathematical Recognition of Scale
- The Territory of Linear Theory
- Linear Space
- The Horizon of Mathematical Science
- The Mathematical Definition of Vectors
- Graphs
- Geometric Representation of Laws
- Exponential Law
- Nonlinearity
- Phenomenology and Structures
- Nonlinear Phenomena
- The Typology of Distortion
- Nonlinearity Emerging in Small Scale
- Singularity
- Nonlinearity Escaping from Linearity
- Criticality
- Bifurcation (Polyvalency) and Discontinuity
- Notes
- Problems
- Solutions
- References
- 2 From Cosmos to Chaos
- The Order of Nature
- A Geometric View
- Galileo's Natural Philosophy
- Geometric Description of Events
- Universality Discovered by Newton
- Function
- The Mathematical Representation of Order
- Motion and Function
- Nonlinear Regime
- Beyond the Functional Representation of Motion
- Decomposition
- Elucidation of Order
- The Mathematical Representation of Causality
- Exponential Law
- A Basic Form of Group
- Resonance
- Undecomposable Motion
- Nonlinear Dynamics
- An Infinite Chain of Interacting Modes
- Chaos
- Motion in the Infinite Period
- Separability/Inseparability
- Invariance in Dynamics
- Constants of Motion
- Chaos
- True Evolution
- Collective Order
- Complete Solution
- The Frame of SpaceEmbodying Order
- The Difficulty of Infinity
- Symmetry and Conservation Law
- Symmetry in Dynamical System
- The Deep Structure of Dynamical System
- The Translation of Motion and Non-motion
- Chaos
- The Impossibility of Decomposition
- Notes
- Problems
- Solutions
- References
- 3 The Challenge of Macro-Systems.
- The Difficulty of Prediction
- Chaos in Phenomenological Recognition
- Stability
- Attractors
- Stability and Integrability
- Randomness as Hypothetical Simplicity
- Stochastic Process
- Representation of Motion by Transition Probability
- H-Theorem
- Statistical Equilibrium
- Statistically Plausible Particular Solutions
- Collective Phenomena
- Nonequilibrium and Macroscopic Dynamics
- A Model of Collective Motion
- A Statistical Model of Collisions
- Notes
- Problems
- Solutions
- References
- 4 Interactions of Micro and Macro Hierarchies
- Structure and Scale Hierarchy
- Crossing-Over Hierarchies
- Connection of Scale Hierarchies
- Structure
- Topology
- A System of Differences
- The Topology of Geometry
- Scale Hierarchy and Topology
- Fractals
- Aggregates of Scales
- The Scale of Event / The Scale of Law
- Scaling and Representation
- Scale Separation
- Spontaneous Selection of Scale by Nonlinearity
- Singularity
- Ideal Limit of Scale-Invariant Structure
- Connections of Scale Hierarchies
- Complexity
- Structures with Multiple Aspects
- Singular Perturbation
- Collaborations of Nonlinearity and Singular Perturbation
- Localized Structures in Space
- Time
- Irreducible Couplings of Multi-Scales
- Notes
- Problems
- Solutions
- References
- Index.