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Counting preimages
2017
Ergodic Theory and Dynamical Systems
For non-invertible maps, subshifts that are mainly of finite type and piecewise monotone interval maps, we investigate what happens if we follow backward trajectories, which are random in the sense that, at each step, every preimage can be chosen with equal probability. In particular, we ask what happens if we try to compute the entropy this way. It turns out that, instead of the topological entropy, we get the metric entropy of a special measure, which we call the fair measure. In general,
doi:10.1017/etds.2016.103
fatcat:5zxu5eyaxnhppgbfi4kt34g374