1 Overview and Basic Concepts

   1.1 Introduction
   1.2 The Programs
   1.3 Literature on Chaotic Dynamics

2 Nonlinear Dynamics and Deterministic Chaos
  
   2.1 Deterministic Chaos
   2.2 Hamiltonian Systems

      2.2.1 Integrable and Ergodic Systems
      2.2.2 Poincare Sections
      2.2.3 The KAM Theorem
      2.2.4 Homoclinic Points

   2.3 Dissipative Dynamical Systems

      2.3.1 Attractors
      2.3.2 Routes to Chaos
 
  2.4 Special Topics

      2.4.1 The Poincare-Birkhoff Theorem
      2.4.2 Continued Fractions
      2.4.3 The Lyapunov Exponent
      2.4.4 Fixed Points of One-Dimensional Maps
      2.4.5 Fixed Points of Two-Dimensional Maps
      2.4.6 Bifurcations

3 Billiard Systems

   3.1 Deformations of a Circle Billiard
   3.2 Numerical Techniques
   3.3 Interacting with the Program
   3.4 Computer Experiments

      3.4.1 From Regularity to Chaos
      3.4.2 Zooming In
      3.4.3 Sensitivity and Determinism
      3.4.4 Suggestions for Additional Experiments
      (Stability of Two-Bounce Orbits / Bifurcations of Periodic Orbits / A New Integrable Billiard?/ Non- Convex Billiards )

   3.5 Suggestions for Further Studies
   3.6 Real Experiments and Empirical Evidence

4 Gravitational Billiards: The Wedge

   4.1 The Poincare Mapping
   4.2 Interacting with the Program
   4.3 Computer Experiments

      4.3.1 Periodic Motion and Phase Space Organization
      4.3.2 Bifurcation Phenomena
      4.3.3 `Plane Filling' Wedge Billiards
      4.3.4 Suggestions for Additional Experiments
      ( Mixed A - B Orbits / Pure B Dynamics / The Stochastic Region / Breathing Chaos )

   4.4 Suggestions for Further Studies
   4.5 Real Experiments and Empirical Evidence

5 The Double Pendulum

   5.1 Equations of Motion
   5.2 Numerical Algorithms
   5.3 Interacting with the Program
   5.4 Computer Experiments

      5.4.1 Different Types of Motion
      5.4.2 Dynamics of the Double Pendulum
      5.4.3 Destruction of Invariant Curves
      5.4.4 Suggestions for Additional Experiments
      ( Testing the Numerical Integration / Zooming In / Different Pendulum Parameters )

   5.5 Real Experiments and Empirical Evidence

6 Chaotic Scattering

   6.1 Scattering off Three Disks
   6.2 Numerical Techniques
   6.3 Interacting with the Program
   6.4 Computer Experiments

      6.4.1 Scattering Functions and Two-Disk Collisions
      6.4.2 Tree Organization of Three-Disk Collisions
      6.4.3 Unstable Periodic Orbits
      6.4.4 Fractal Singularity Structure
      6.4.5 Suggestions for Additional Experiments
      ( Long-Lived Trajectories / Incomplete Symbolic Dynamics / Multiscale Fractals )

   6.5 Suggestions for Further Studies
   6.6 Real Experiments and Empirical Evidence

7 Fermi Acceleration

   7.1 Fermi Mapping
   7.2 Interacting with the Program
   7.3 Computer Experiments

      7.3.1 Exploring Phase Space for Different Wall Oscillations
      7.3.2 KAM Curves and Stochastic Acceleration
      7.3.3 Fixed Points and Linear Stability
      7.3.4 Absolute Barriers
      7.3.5 Suggestions for Additional Experiments
      ( Higher Order Fixed Points / Standard Mapping / Bifurcation Phenomena / Influence of Different Wall Velocities )

   7.4 Suggestions for Further Studies
   7.5 Real Experiments and Empirical Evidence

8 The Duffing Oscillator

   8.1 The Duffing Equation
   8.2 Numerical Techniques
   8.3 Interacting with the Program
   8.4 Computer Experiments

      8.4.1 Chaotic and Regular Oscillations
      8.4.2 The Free Duffing Oscillator
      8.4.3 Anharmonic Vibrations: Resonances and Bistability
      8.4.4 Coexisting Limit Cycles and Strange Attractors
      8.4.5 Suggestions for Additional Experiments
      ( Harmonic Oscillator / Gravitational Pendulum / Exact Harmonic Response / Period-Doubling Bifurcations / Strange Attractors )
 
   8.5 Suggestions for Further Studies
   8.6 Real Experiments and Empirical Evidence

9 Feigenbaum Scenario

   9.1 One-Dimensional Maps
   9.2 Interacting with the Program
   9.3 Computer Experiments

      9.3.1 Period-Doubling Bifurcations
      9.3.2 The Chaotic Regime
      9.3.3 Lyapunov Exponents
      9.3.4 The Tent Map
      9.3.5 Suggestions for Additional Experiments
      ( Different Mapping Functions / Periodic Orbit Theory / Exploring the Circle Map )

   9.4 Suggestions for Further Studies
   9.5 Real Experiments and Empirical Evidence

10 Nonlinear Electronic Circuits

   10.1 A Chaos Generator
   10.2 Numerical Techniques
   10.3 Interacting with the Program
   10.4 Computer Experiments

      10.4.1 Hopf Bifurcation
      10.4.2 Period Doubling
      10.4.3 Return Map
      10.4.4 Suggestions for Additional Experiments
      ( Comparison with an Electronic Circuit / Deviations from the Logistic Mapping / Boundary Crisis )

   10.5 Real Experiments and Empirical Evidence

11 Mandelbrot and Julia Sets

   11.1 Two-Dimensional Iterated Maps
   11.2 Numerical and Coloring Algorithms
   11.3 Interacting with the Program
   11.4 Computer Experiments
 
      11.4.1 Mandelbrot and Julia Sets
      11.4.2 Zooming into the Mandelbrot Set
      11.4.3 General Two-Dimensional Quadratic Mappings

   11.5 Suggestion for Additional Experiments
   ( Components of the Mandelbrot Set / Distorted Mandelbrot Maps / Further Experiments )
   11.6 Real Experiments and Empirical Evidence

12 Ordinary Differential Equations

   12.1 Numerical Techniques
   12.2 Interacting with the Program
   12.3 Computer Experiments

      12.3.1 The Pendulum
      12.3.2 A Simple Hopf Bifurcation
      12.3.3 The Duffing Oscillator Revisited
      12.3.4 Hill's Equation
      12.3.5 The Lorenz Attractor
      12.3.6 The Rössler Attractor
      12.3.7 The Henon-Heiles System
      12.3.8 Suggestions for Additional Experiments
      ( Lorenz System: Limit Cycles and Intermittency / The Restricted Three Body Problem )

   12.4 Suggestions for Further Studies

13 Kicked Systems

   13.1 Interacting with the Program
   13.2 Computer Experiments

      13.2.1 The Standard Mapping
      13.2.2 The Kicked quatric Oscillator
      13.2.3 The Kicked quatric Oscillator with damping
      13.3.4 The henon Map
      13.2.5 Suggestions for Additional Experiments

   13.3 Real Experiments and Empirical Evidence

Appendix A: System Requirements and Program Installation

   A.1 System Requirements
   A.2 Installing the Programs

      A.2.1 Windows Operating System
      A.2.2 Linux Operating System
  
   A.3 Programs
   A.4 Third Party Software

Appendix B: General Remarks on Using the Programs

   B.1 Interaction with the Programs
   B.2 Input of Mathematical Expressions

Glossary