Introduction To Chaotic Dynamical Systems

Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his PhD from the University of California at Berkeley in under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets. He is also the author of A First Course in Chaotic Dynamical Systems, Second Edition, published by CRC Press.

• I One Dimensional Dynamics1.A Visual and Historical Tour2.Examples of Dynamical Systems3.Elementary Definitions4.Hyperbolicity5.An Example: The Logistic Family6.Symbolic Dynamics7.Topological Conjugacy8.Chaos9.Structural Stability10.Sharkovsky's Theorem11.The Schwarzian Derivative 12.Bifurcations13.Another View of Period Three14.Period-Doubling Route to Chaos15.Homoclinic Points and Bifurcations16.Maps of the Circle17.Morse-Smale DiffeomorphismsII Complex Dynamics18.Quadratic Maps Revisited19.Normal Families and Exceptional Points 20.Periodic Points21.Properties of the Julia Set22.The Geometry of the Julia Sets23.Neutral Periodic Points24.The Mandelbrot Set25.Rational Maps26.The Exponential FamilyIII Higher Dimensional Dynamics27.Dynamics of Linear Maps28.The Smale Horseshoe Map29.Hyperbolic Toral Automorphisms30.Attractors31.The Stable and Unstable Manifold Theorem32.Global Results and Hyperbolic Maps33.The Hopf Bifurcation34.The Herron MapAppendix: Mathematical Preliminaries