This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics, 2)

Wiggins, Stephen

Reference

Springer

Written jointly by a specialist in geophysical fluid dynamics and an applied mathematician, this is the first accessible introduction to a new set of methods for analysing Lagrangian motion in geophysical flows. The book opens by establishing context and fundamental mathematical concepts and definitions, exploring simple cases of steady flow, and touching on important topics from the classical theory of Hamiltonian systems. Subsequent chapters examine the elements and methods of Lagrangian transport analysis in time-dependent flows. The concluding chapter offers a brief survey of rapidly evolving research in geophysical fluid dynamics that makes use of this new approach.

Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (Interdisciplinary Applied Mathematics, 31)

Samelson, Roger M.

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Applied Mathematical Sciences, 105)

In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.

Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (Applied Mathematical Sciences, 128)

Science & Math

Li, Charles

Mathematics

Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.

Chaotic Transport in Dynamical Systems (Interdisciplinary Applied Mathematics, 2)

Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions.

The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids (Cambridge Monographs on ... Computational Mathematics, Series Number 22)

Sturman, Rob

Ottino, Julio M.

Cambridge University Press

Written by a specialist in geophysical fluid dynamics and an applied mathematician, this book provides an accessible introduction to new methods for analysing Lagrangian motion in geophysical flows, and surveys research in geophysical fluid dynamics that makes use of them.

Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.

Chaotic Transport in Dynamical Systems (Interdisciplinary Applied Mathematics)

Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.

Global Bifurcations and Chaos: Analytical Methods (Applied Mathematical Sciences, 73)

See the best price to sell, buy, or rent books by Wiggins, Stephen. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Wiggins, Stephen

See the best price to sell, buy, or rent books by Wiggins, Stephen. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics, 2)

Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (Interdisciplinary Applied Mathematics, 31)

Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Applied Mathematical Sciences, 105)

Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (Applied Mathematical Sciences, 128)

Chaotic Transport in Dynamical Systems (Interdisciplinary Applied Mathematics, 2)

The Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications: Micro to Macro, Fluids to Solids (Cambridge Monographs on ... Computational Mathematics, Series Number 22)

Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics, 2)

Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (Interdisciplinary Applied Mathematics, 31)

Chaotic Transport in Dynamical Systems (Interdisciplinary Applied Mathematics)

Global Bifurcations and Chaos: Analytical Methods (Applied Mathematical Sciences, 73)