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A common fixed point of commuting mappings of a tree. (English. Russian original) Zbl 1119.54328
Mosc. Univ. Math. Bull. 57, No. 6, 1-8 (2002); translation from Vestn. Mosk. Univ., Ser. I 2002, No. 6, 3-10 (2002).
In the paper it is proved that if two commuting mappings of a segment do not have a common fixed point, then their composition entropy is not less than 2. Also mappings on a snake-like continuum are discussed as well as some related problems.
The annotated bibliography contains 69 entries.

54H25 Fixed-point and coincidence theorems (topological aspects)
37E25 Dynamical systems involving maps of trees and graphs
54F15 Continua and generalizations
55M20 Fixed points and coincidences in algebraic topology