Invariant densities for  piecewise linear maps of  interval

The newest addition: Mathematica 8 program to find invariant densities.
Written by Camilo Ortiz <camiloortiza-at-gmail.com>

preprint   updated February 6, 2008. This is an old version, can be useful as it contains
                the proof of the main theorem in a simple case of greedy maps
new preprint   March 17, 2008.  Contains the proof for piecewise increasing in whole generality.

The newest preprint  updated at the end of July, 2008. Contains proof for arbitrary piecewise linear maps and some other improvements.

Presentation, pdf.



Maple programs for old version and their pdf printouts:

          

Programs in Maple 11 : to download right click and "Save target as..." or something similar	Pdf printouts
map with 3 branches
map with more branches	pdf
general greedy map Example 2	pdf
lazy map and conjugated Example 4	pdf
mixed map Example 5	pdf
Parry's map Example 6	pdf
mixed map Example 7  :  case 1 , case 2	pdf1  , pdf2
mixed map Example 8	pdf
map with hanging branches Example 9	pdf
hanging Example 10	pdf
ALL  MAPLE PROGRAMS ZIPPED TOGETHER FOR EASY DOWNLOAD

Maple programs for NEW version and their pdf printouts: the numbering in the newest preprint is
 shifted by 1.

Example 1	Example 1_pdf
Example 2	Example 2_pdf
Example 3	Example 3_pdf
Example 4	Example 4_pdf
Example 5	Example 5_pdf
Example 6	Example 6_pdf
Example 9	Example 9_pdf
Example 11	Example 11_pdf
ALL  MAPLE NEW PROGRAMS ZIPPED TOGETHER FOR EASY DOWNLOAD

There are two Maple program added in the newest preprint:

Example 1:
Maple program                              PDF printout

Example showing that conjecture 1 fails for not piecewise increasing maps:

Maple program                               PDF printout

Here is an additional example : invariant density for generalized beta map (before we were
not able to always find it if the map was of (alpha,beta) type )
Maple program                              PDF printout