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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
*x*_{0} for different choices of *x*_{0},
and studied what happens as you vary
. 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

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