Probability density functions (PDF's) have inherent connections to the field of Dynamical Systems.

The motivation for this question can be found in: http://www.stat.cmu.edu/~cshalizi/754/2006/notes/solutions-2.pdf for the logistic map when $x∈[0,1]$.

My question is:

Is it possible to define the density of the logistic map for $x<0$ where the map convegres to $-∞$?