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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.

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

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/s …