Chaos, Nonlinearity, Complexity

I think the next century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don't know how the laws ?t together, and what happens under extreme conditions. But I expect we will ?nd a complete uni?ed theory sometime this century. There is no limit to the complexity that we can build using those basic laws. Stephen Hawking, January 2000. We don't know what we are talking about. Many of us believed that string theory was a very dramatic break with our previous notions of quantum theory. But now we learn that string theory, well, is not that much of a break. The state of physics today is like it was when we were mysti?ed by radioactivity. They were missing something absolutely fundamental. We are missing perhaps something as profound as they were back then. Nobel Laureate David Gross, December 2005. This volume is essentially a compilation of papers presented at the Int- national Workshop on Mathematics and Physics of Complex and Nonlinear Systems that was held at Indian Institute of Technology Kanpur, March 14 26, 2004 on the theme ChaNoXity: The Nonlinear Dynamics of Nature.

Carefully edited and selected outcome of the international workshop IIT held in Kanpur, India March 2004 featuring a focused debate on the mathematics and physics of Chaos, complexity and the Nonlinear Dynamics of Nature Presents an overview of the strong nonlinearity of chaos and complexity in natural systems Motivates teaching and research of nonlinear sciences in educational and research institutions Includes supplementary material: sn.pub/extras

Texte du rabat

This carefully edited book presents a focused debate on the mathematics and physics of chaos, nonlinearity and complexity in nature. It explores the role of non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems that draws on the relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It presents a self-contained scientific theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.

Contenu
Chaos, Periodicity and Complexity on Dynamical Systems.- Foundations of Nonextensive Statistical Mechanics.- Critical Attractors and the Physical Realm of q-statistics.- Non-Boltzmannian Entropies for Complex Classical Systems, Quantum Coherent States and Black Holes.- Power Law and Tsallis Entropy: Network Traffic and Applications.- The Role of Chaos and Resonances in Brownian Motion.- Models of Finite Bath and Generalised Thermodynamics.- Quantum Black Hole Thermodynamics.- Complexity in Organizations: A Paradigm Shift.- Chaos, Nonlinearity, Complexity: A Unified Perspective.