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An Introduction to Chaotic Dynamical Systems
- Part One: One-Dimensional Dynamics
- Examples of Dynamical Systems
- Preliminaries from Calculus
- Elementary Definitions
- Hyperbolicity
- An example: the quadratic family
- An Example: the Quadratic Family
- Symbolic Dynamics
- Topological Conjugacy
- Chaos
- Structural Stability
- Sarlovskii’s Theorem
- The Schwarzian Derivative
- Bifurcation Theory
- Another View of Period Three
- Maps of the Circle
- Morse-Smale Diffeomorphisms
- Homoclinic Points and Bifurcations
- The Period-Doubling Route to Chaos
- The Kneeding Theory
- Geneaology of Periodic Units
- Part Two: Higher Dimensional Dynamics
- Preliminaries from Linear Algebra and Advanced Calculus
- The Dynamics of Linear Maps: Two and Three Dimensions
- The Horseshoe Map
- Hyperbolic Toral Automorphisms
- Hyperbolicm Toral Automorphisms
- Attractors
- The Stable and Unstable Manifold Theorem
- Global Results and Hyperbolic Sets
- The Hopf Bifurcation
- The Hénon Map
- Part Three: Complex Analytic Dynamics
- Preliminaries from Complex Analysis
- Quadratic Maps Revisited
- Normal Families and Exceptional Points
- Periodic Points
- The Julia Set
- The Geometry of Julia Sets
- Neutral Periodic Points
- The Mandelbrot Set
- An Example: the Exponential Function
Dummy View - NOT TO BE DELETED