I One Dimensional Dynamics
1.A Visual and Historical Tour
2.Examples of Dynamical Systems
3.Elementary Definitions
4.Hyperbolicity
5.An Example: The Logistic Family
6.Symbolic Dynamics
7.Topological Conjugacy
8.Chaos
9.Structural Stability
10.Sharkovsky's Theorem
11.The Schwarzian Derivative
12.Bifurcations
13.Another View of Period Three
14.Period-Doubling Route to Chaos
15.Homoclinic Points and Bifurcations
16.Maps of the Circle
17.Morse-Smale Diffeomorphisms
II Complex Dynamics
18.Quadratic Maps Revisited
19.Normal Families and Exceptional Points
20.Periodic Points
21.Properties of the Julia Set
22.The Geometry of the Julia Sets
23.Neutral Periodic Points
24.The Mandelbrot Set
25.Rational Maps
26.The Exponential Family
III Higher Dimensional Dynamics
27.Dynamics of Linear Maps
28.The Smale Horseshoe Map
29.Hyperbolic Toral Automorphisms
30.Attractors
31.The Stable and Unstable Manifold Theorem
32.Global Results and Hyperbolic Maps
33.The Hopf Bifurcation
34.The Herron Map
Appendix: Mathematical Preliminaries
Biography
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.
