**CHAPTER 37A Characterization of Dark Risk**

The difficulty with modeling markets in a dynamical way is that their essence is free human choice, whereas the central core of dynamical systems is determinism. *Determinism* means that the past determines the future and, as will be demonstrated, vice versa. This definition implies that zero topologic entropy is a requirement for predictability. This will take some unpacking.

**THEOREM (KAMINSKI)1**

A system (*X, T*) is *topologically predictable* if for every continuous function *f* in *C*(*X*) we have *f* in <1, *T, f, T*^{2}, *f*, …> where <*F*> *⊂ C* (*X*) denotes the closed algebra generated by a family *F ⊂ C* (*X*). (*X, T*) is topologically predictable if and only if every factor of (*X, T*) is invertible, where a factor is a system ...

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