To learn tests of chaos in experimental data, we first analyze
the dynamics of iterates of some simple functions. In general, given a function f(x),
we are interested in predicting the longterm behavior of the orbit 
x_{0}, x_{1} = f(x_{0}), x_{2} = f(x_{1}) =
f^{2}(x_{0}), x_{3} = f(x_{2}) = f^{3}(x_{0}), ... 
of the point x_{0}. 
Can we predict any features of this orbit without
computing the x_{i}? 
How does the longterm behavior of the orbit depend on the choice
of initial value x_{0}? 
We shall study these and related questions for these test functions 
The Tent Map is one of the
simplest of nonlinear maps, its graph is just two straight lines. 

The Logistic Map is a model for a
population growing in an environment with limited resources. Amazingly, there are
questions about these parabolas that cannot be answered. 

