Differential Equations, Dynamical Systems, and an Introduction to Chaos, Volume 60Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems. * Developed by awardwinning researchers and authors * Provides a rigorous yet accessible introduction to differential equations and dynamical systems * Includes bifurcation theory throughout * Contains numerous explorations for students to embark upon NEW IN THIS EDITION * New contemporary material and updated applications * Revisions throughout the text, including simplification of many theorem hypotheses * Many new figures and illustrations * Simplified treatment of linear algebra * Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor * Increased coverage of discrete dynamical systems 
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Review: Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)
User Review  Joecolelife  Goodreadsthis is an excellent introduction for beginners. in fact, this reference has explained the differential equations, the dynamical system and the chaos as clear as possible. the elementary mathematical ... Read full review
Review: Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics)
User Review  Joecolelife  Goodreadsthis is an excellent introduction for beginners. in fact, this reference has explained the differential equations, the dynamical system and the chaos as clear as possible. the elementary mathematical ... Read full review
Contents
Chapter 1 FirstOrder Equations  1 
Chapter 2 Planar Linear Systems  21 
Chapter 3 Phase Portraits for Planar Systems  39 
Chapter 4 Classification of Planar Systems  61 
Chapter 5 Higher Dimensional Linear Algebra  75 
Chapter 6 Higher Dimensional Linear Systems  107 
Chapter 7 Nonlinear Systems  139 
Chapter 8 Equilibria in Nonlinear Systems  159 
Chapter 11 Applications in Biology  235 
Chapter 12 Applications in Circuit Theory  257 
Chapter 13 Applications in Mechanics  277 
Chapter 14 The Lorenz System  303 
Chapter 15 Discrete Dynamical Systems  327 
Chapter 16 Homoclinic Phenomena  359 
Chapter 17 Existence and Uniqueness Revisited  383 
407  
Common terms and phrases
assume asymptotically stable attractor basic regions behavior of solutions bifurcations that occur canonical form Chapter circle closed orbit compute conjugacy Consider the system constant continuous coordinates defined denote dense Describe differential equations distinct eigenvalues dynamical systems eigenvalues eigenvector equilibrium point example exp(tA Figure ﬁnd firstorder fixed point flow follows given graph harmonic oscillator Hence horseshoe map initial condition initial value problem iteration Liapunov function limit cycle linear map linearized system linearly independent logistic Lorenz system matrix nonautonomous nonlinear system Note nullclines open set origin parameter periodic points periodic solution phase portrait planar system plane Poincaré map population Proof Proposition Prove saddle sequence sink slope solution curve solution X(t solutions tend solve spiral subset subspace Suppose system of differential system X tangent theorem unstable curve vector field vector field points