Chaos and nonlinear dynamics An introduction for scientists and engineers

By: Hilborn, Robert CMaterial type: TextTextPublication details: New York: Oxford Uni. Press, [c2009]Description: 650 pISBN: 9780198507239LOC classification: Q 172.5.C
Contents:
I THE PHENOMENOLOGY OF CHAOS 1 Three Chaotic Systems 2 The Universality of Chaos II TOWARD A THEORY OF NONLINEAR DYNAMICS AND CHAOS 3 Dynamics in State Space: One and Two Dimensions 4 Three-Dimensional State Space and Chaos 5 Iterated Maps 6 Quasi-Periodicity and Chaos 7 Intermittency and Crises 8 Hamiltonian Systems III MEASURES OF CHAOS 9 Quantifying Chaos 10 Many Dimensions and Multifractals IV SPECIAL TOPICS 11 Pattern Formation and Spatiotemporal Chaos 12 Quantum Chaos, The Theory of Complexity, and Other Topics
Summary: This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a detailed derivation of the famous Feigenbaum numbers). It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. Important tools such as Lyapunov exponents, fractal dimensions, and correlation dimensions are treated in detail. Several appendices provide a detailed derivation of the Lorenz model from the Navier-Stokes equation, a summary of bifurcation theory, and some simple computer programs to study nonlinear dynamics. Each chapter includes an extensive, annotated bibliography.
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General Sc Rack No 3 Q 172.5.C (Browse shelf (Opens below)) Available Invoice no. IN 1300 ; Date: 31-12-2019 02333
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I THE PHENOMENOLOGY OF CHAOS
1 Three Chaotic Systems
2 The Universality of Chaos

II TOWARD A THEORY OF NONLINEAR DYNAMICS AND CHAOS
3 Dynamics in State Space: One and Two Dimensions
4 Three-Dimensional State Space and Chaos
5 Iterated Maps
6 Quasi-Periodicity and Chaos
7 Intermittency and Crises
8 Hamiltonian Systems

III MEASURES OF CHAOS
9 Quantifying Chaos
10 Many Dimensions and Multifractals

IV SPECIAL TOPICS
11 Pattern Formation and Spatiotemporal Chaos
12 Quantum Chaos, The Theory of Complexity, and Other Topics

This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a detailed derivation of the famous Feigenbaum numbers). It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. Important tools such as Lyapunov exponents, fractal dimensions, and correlation dimensions are treated in detail. Several appendices provide a detailed derivation of the Lorenz model from the Navier-Stokes equation, a summary of bifurcation theory, and some simple computer programs to study nonlinear dynamics. Each chapter includes an extensive, annotated bibliography.

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