Differential Equations and Dynamical Systems [3 ed.] 1461300037, 9781461300038

Table of contents :
Cover
Series Preface
Preface to the Third Edition
Contents
1 Linear Systems
1.1 Uncoupled Linear Systems
1.2 Diagonalization
1.3 Exponentials of Operators
1.4 The Fundamental Theorem for Linear Systems
1.5 Linear Systems in R^2
1.6 Complex Eigenvalues
1.7 Multiple Eigenvalues
1.8 Jordan Forms
1.9 Stability Theory
1.10 Nonhomogeneous Linear Systems
2 Nonlinear Systems: Local Theory
2.1 Some Preliminary Concepts and Definitions
2.2 The Fundamental Existence-Uniqueness Theorem
2.3 Dependence on Initial Conditions and Parameters
2.4 The Maximal Interval of Existence
2.5 The Flow Defined by a Differential Equation
2.6 Linearization
2.7 The Stable Manifold Theorem
2.8 The Hartman-Grobman Theorem
2.9 Stability and Liapunov Functions
2.10 Saddles, Nodes, Foci and Centers
2.11 Nonhyperbolic Critical Points in R^2
2.12 Center Manifold Theory
2.13 Normal Form Theory
2.14 Gradient and Hamiltonian Systems
3 Nonlinear Systems: Global Theory
3.1 Dynamical Systems and Global Existence Theorems
3.2 Limit Sets and Attractors
3.3 Periodic Orbits, Limit Cycles and Separatrix Cycles
3.4 The Poincaré Map
3.5 The Stable Manifold Theorem for Periodic Orbits
3.6 Hamiltonian Systems with Two Degrees of Freedom
3.7 The Poincaré-Bendixson Theory in R^2
3.8 Lienard Systems
3.9 Bendixson's Criteria
3.10 The Poincaré Sphere and the Behavior at Infinity
3.11 Global Phase Portraits and Separatrix Configurations
3.12 Index Theory
4 Nonlinear Systems: Bifurcation Theory
4.1 Structural Stability and Peixoto's Theorem
4.2 Bifurcations at Nonhyperbolic Equilibrium Points
4.3 Higher Codimension Bifurcations at Nonhyperbolic Equilibrium Points
4.4 Hopf Bifurcations and Bifurcations of Limit Cycles from a Multiple Focus
4.5 Bifurcations at Nonhyperbolic Periodic Orbits
4.6 One-Parameter Families of Rotated Vector Fields
4.7 The Global Behavior of One-Parameter Families of Periodic Orbits
4.8 Homoclinic Bifurcations
4.9 Melnikov's Method
4.10 Global Bifurcations of Systems in R^2
4.11 Second and Higher Order Melnikov Theory
4.12 Françoise's Algorithm for Higher Order Melnikov Functions
4.13 The Takens-Bogdanov Bifurcation
4.14 Coppel's Problem for Bounded Quadratic Systems
4.15 Finite Codimension Bifurcations in the Class of Bounded Quadratic Systems
References
Additional References
Index

Polecaj historie

Differential Equations, Dynamical Systems, and Linear Algebra 9780080873763, 0080873766

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and

2,364 317 11MB Read more

Introduction to Differential Equations with Dynamical Systems 9781400841325

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduct

196 99 5MB Read more

Differential Equations: From Calculus to Dynamical Systems 1470444003, 9781470444006

3,951 566 5MB Read more

Non-Linear Differential Equations and Dynamical Systems [1 ed.] 0367137194, 9780367137199

  This fourth volume in the series "Mathematics and Physics Applied to Science and Technology": (i) follows th

929 205 7MB Read more

Ordinary differential equations and dynamical systems 978-0-8218-8328-0, 0821883283

667 141 3MB Read more

Differential Equations, Dynamical Systems, and an Introduction to Chaos [3rd edition] 9780123820112, 0123820111

Chapter 1 First-order equations -- chapter 2 Planar linear systems -- chapter 3 Phase portraits for planar systems -- ch

1,338 190 6MB Read more

A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems [2]

199 19 19MB Read more

Differential equations, dynamical systems, and an introduction to chaos [3. ed] 9780123820105, 2012002951, 0123820103

Hirsch, Devaney, and Smale's classicDifferential Equations, Dynamical Systems, and an Introduction to Chaoshas been

1,045 217 6MB Read more

Differential Equations

292 108 1MB Read more

Volterra and Functional Differential Equations

This book contains twenty four papers, presented at the conference on Volterra and Functional Differential Equations hel

247 73 20MB Read more