I have written `logmap` for an collegue of mine. I wanted to
show him that the numerical computation of the limit cycles can be
speed-up and improved in quality by some kind of shooting method.
### Function

The program logmap computes the bifurcation diagram and the Lyapunov
exponents of the logistic map
$x(n+1)\; =\; \lambda \; x(n)\; (\; 1.0\; +\; x(n)\; )$
with the bifurcation parameter
$\lambda \in [0.5,4]$. Below you can see the graphs of the computed data.
### Installation

To install the package you need a **linux box, a gcc compiler, and
gnuplot**.

Get the file logmap.tgz and extract it by

`
tar -xzvf logmap.tgz
`

The archive file `logmap.tgz`
extracts into a directory `Logmap` relative to the current
path. Change to that directory and call

`
make all
`

that should create the eps-files `traj.eps` and
`lyap.eps` with the bifurcation diagram and the graph of the
Lyapunov exponent versus λ. Both pictures are shown below.