
*** vanderpl ***

This is an example of a cubical map generated for the Van der Pol
equations embedded in R^3. An isolating neighbourhood of an attracting
trajectory was chosen here and a map corresponding to a discretization
of the dynamical system was generated. Each cube is mapped into
a rectangular set in R^3 (a prism) contained in this neighbourhood.

Method 1. We first verify that the map is almost perfect with the program 
"chkperf". Then the program "chmap" is used to create a chain map for 
homology computation. The result of the program is trsnsformed into 
a purely algebraic chain map by the program "cnvchmap". Finally, the program 
"homchain" computes the map induced in homology. Note that the basis found 
in the codomain may be different from the basis found in the domain of the map.

Method 2. We use the program "homcubes" directly. We first verify with the 
program "chkmvmap" that the map satisfies the necessary assumptions, and then 
we compute the map itself with "homcubes". Note that since we have the map 
induced by the inclusion in homology, we know how the generators in the 
domain of the map are related to the generators in the codomain of the map.
