[FOM] About ln |x|

[Harvey Friedman]

On 2/9/04 4:58 PM, "Adam Epstein" <adame at maths.warwick.ac.uk> wrote:

> I don't now anything about the status of these questions. But matters such
> as these are already an issue for much more basic (if less physical)
> dynamical systems. For example, consider the one-parameter familiy of
> polynomial maps x->x^2+c. These are often studied over C (yielding
> Julia sets and the Mandelbrot set) but for now restrict attention to real
> values of x and real parameters c.
> 
If we are going to be talking about function iteration, then here is a
favorite of mine. (I like yours too).

In calculus, one considers the map from R\{0} into R given by

f(x) = ln |x|.

QUESTION: Is the orbit of 2 finite or infinite?

There are endless questions one can ask about the set of x such that the
orbit of x is finite.

I have not heard of any nontrivial results about this.

Harvey Friedman