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The Mathematica Programmer: Function Iteration and Chaos

Roman Maeder
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Journal / Anthology

The Mathematica Journal
Year: 1995
Volume: 5
Issue: 2
Page range: 28-40

We present a number of programs to investigate and visualize chaos as it occurs with iterated application of functions. We look at ways to picture orbits under repeated application and to draw final-state diagrams. We discuss symbolic and numerical methods to find periodic orbits, bifurcation points, super-attractive orbits, and the Feigenbaum constant. Further topics include statistical analysis and visualization of chaotic phenomena such as sensitivity, mixing, ergodic orbits, and intermittency.

*Mathematics > Calculus and Analysis > Dynamical Systems


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