🚀 go-pugleaf

The solution proposed by Arthur Rubin in sci.math.research is perfectly
correct.  However, I'd like to have a less degenerate exemple. One might
perhaps add a condition like

"all the variables x_1,...,x_n must occur in each P_i"

or a similar but weaker condition like 

"The set of variables {1,...,n} cannot be partitioned in two subsets I1 and
I2 such that the two subsystems (x_i)_{i in I1} and (x_i)_{i in I2} evolve
independently from each other".

The motivation behind my question is to find a dynamical property
differentiating piecewise-linear functions from polynomial, rational, or
analytic function on [0,1]^n. Any suggestion on this is welcome. For n=2,
there exist non degenerate piecewise-linear functions with infinitely many
k-cycles for every k (hence my question).

Pascal.