Something dynamics can tell us about number theory
Here we sketch an example of how techniques from dynamics can be applied to derive results from number theory. Details can be found
here
.
First we review the necessary tools from dynamics:
graphical iteration
,
fixed points
, and
cycles
.
Here is the
family of functions
we use.
Now we
count the periodic points
of the functions.
Finally, we apply
counting
to derive a well-known result from number theory.