**"Mathematics of Complexity and Dynamical Systems" ed. by Robert A. Meyers**

*Springer Reference. Encyclopedia of Complexity and Systems Science*

Sрringеr | 2012 | ISBN: 1461418054 9781461418061 9781461418078 9781461418054 | 1888 pages | PDF | 35 MB

This is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. This book is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers

The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics.

**Table of Contents** Contributors

Adomian Decomposition Method Applied to Non-linear Evolution Equations in Soliton Theory

Anomalous Diffusion on Fractal Networks

Biological Fluid Dynamics, Non-linear Partial Differential Equations

Catastrophe Theory

Center Manifolds

Chaos and Ergodic Theory

Chronological Calculus in Systems and Control Theory

Control of Non-linear Partial Differential Equations

Diagrammatic Methods in Classical Perturbation Theory

Discrete Control Systems

Dispersion Phenomena in Partial Differential Equations

Dynamics on Fractals

Dynamics of Parametric Excitation

Entropy in Ergodic Theory

Ergodicity and Mixing Properties

Ergodic Theorems

ErgodicTheory:BasicExamplesand Constructions

Ergodic Theory: Fractal Geometry

Ergodic Theory on Homogeneous Spaces and Metric Number Theory

Ergodic Theory: Interactions with Combinatorics and Number Theory

Ergodic Theory, Introduction to

Ergodic Theory: Non-singular Transformations

Ergodic Theory: Recurrence

Ergodic Theory: Rigidity

Existence and Uniqueness of Solutions of Initial Value Problems

Finite Dimensional Controllability

Fractal Geometry, A Brief Introduction to

Fractal Growth Processes

Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks

Fractal and Multifractal Time Series

Fractals in Biology

Fractals and Economics

Fractals in Geology and Geophysics

Fractals Meet Chaos

Fractals and Percolation

Fractals in the Quantum Theory of Spacetime

Fractal Structures in Condensed Matter Physics

Fractals and Wavelets: What Can We Learn on Transcription and Replication from Wavelet-Based Multifractal Analysis of DNASequen

Fractal and Transfractal Scale-Free Networks

Hamiltonian Perturbation Theory (and Transition to Chaos)

Hamilton^Jacobi Equations and Weak KAM Theory

Hybrid Control Systems

Hyperbolic Conservation Laws

Hyperbolic Dynamical Systems

Infinite Dimensional Controllability

Inverse Scattering Transform and the Theory of Solitons

Isomorphism Theory in Ergodic Theory

Joinings in Ergodic Theory

Kolmogorov^-Arnold-Moser (KAM) Theory

Korteweg-de Vries Equation (KdV), Different Analytical Methods for Solving the

Korteweg-de Vries Equation (KdV), History, Exact N-Soliton Solutions and Further Properties of the

Korteweg-de Vries Equation (KdV) and Modified Korteweg-de Vries Equations (mKdV), Semi-analytical Methods for Solving the

Korteweg-de Vries Equation (KdV), Some Numerical Methods for Solving the

Learning, System Identification, and Complexity

Lyapunov-Schmidt Method for Dynamical Systems

Maximum Principle in Optimal Control

Measure Preserving Systems

Mechanical Systems: Symmetries and Reduction

Navier-Stokes Equations: A Mathematical Analysis

-Body Problem and Choreographies

Nekhoroshev Theory

Non-linear Dynamics, Symmetry and Perturbation Theory in

Non-linear Internal Waves

Non-linear Ordinary Differential Equations and Dynamical Systems, Introduction to

Non-linear Partial Differential Equations, Introduction to

Non-linear Partial Differential Equations, Viscosity Solution Method in

Non-linear Stochastic Partial Differential Equations

Nonsmooth Analysis in Systems and Control Theory

Normal Forms in Perturbation Theory

Numerical Bifurcation Analysis

Observability (Deterministic Systems) and Realization Theory

Partial Differential Equations that Lead to Solitons

Periodic Orbits of Hamiltonian Systems

Periodic Solutions of Non-autonomous Ordinary Differential Equations

Perturbation Analysis of Parametric Resonance

Perturbation of Equilibria in the Mathematical Theory of Evolution

Perturbation of Systems with Nilpotent Real Part

Perturbation Theory

Perturbation Theory in Celestial Mechanics

Perturbation Theory. Introduction to

Perturbation Theory and Molecular Dynamics

Perturbation Theory for Non-smooth Systems

Perturbation Theory for PDEs

Perturbation Theory in Quantum Mechanics

Perturbation Theory. Semiclassical

Perturbative Expansions. Convergence of

Phase Transitions on Fractals and Networks

Philosophy of Science. Mathematical Models in

Pressure and Equilibrium States in Ergodic Theory

Quantum Bifurcations

Reaction Kinetics in Fractals

Relaxation Oscillations

Robotic Networks, Distributed Algorithms for

Scaling Limits of Large Systems of Non-linear Partial Differential Equations

Shallow Water Waves and Solitary Waves

Smooth Ergodic Theory

Soliton Perturbation

Solitons and Compactons

Solitons: Historical and Physical Introduction

Solitons Interactions

Solitons. Introduction to

Solitons, Tsunamis and Oceanographical Applications of

Spectral Theory of Dynamical Systems

Stability and Feedback Stabilization

Stability Theory of Ordinary Differential Equations

Stochastic Noises, Observation, Identification and Realization with

Symbolic Dynamics

System Regulation and Design, Geometric and Algebraic Methods in

Systems and Control, Introduction to

Topological Dynamics

Vehicular Traffic: A Review of Continuum Mathematical Models

Water Waves and the Korteweg-de Vries Equation

List of Glossary Terms

Index

with TOC BookMarkLinks

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