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One-Dimensional Dynamical Systems

Part 4: Linear and Nonlinear Behavior

In the first part of this course you investigated the eventual behavior of the Logistic map. That is, you investigated the orbit of x₀ for different choices of x₀, and studied what happens as you vary lambda

. In the second part of thi course we take a more mathematical viewpoint and not only describe what happens, but also ask ourselves why this happens.

Linear versus nonlinear

Periodic points
Eventual behavior
Hartman and Grobman

The phenomenon where an attracting fixed point becomes repelling, and at the same time an attracting periodic orbit of period 2 appears, is called period-doubling. It is an example of a bifurcation.

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Created: Apr 3 1998 --- Last modified: Wed Apr 8 19:22:07 1998