Localizing the Lef schetz number of certain chain approximations of upper semi continuous multivalued mappings a new approach to fixed point index is given. It turns out that this fixed point index satisfies the commutativity property as well as the mod-p property (known from the singlevalued case). In particular, in the single-valued case the proof of the mod-p property is a natural consequence of a corresponding property of (global) Lefschetz number.

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This paper establishes a global dynamical systems approach for the fractal patterns which are obtained when analysing the divisibility of binomial coefficients modulo a prime power. The general framework is within the class of hierarchical iterated function systems. As a consequence we obtain a complete deciphering of the hierarchical self-similarity features. F. v. Haeseler et al. fk.rfw Xkccw XkEKk. rTW E*tL. tTk. T L EPkkkk. rFk.ttk.ttb