| Abstract: | The notion of elementary map of a dendrite into itself is introduced. Arithmetical relations between the periods of periodic points are given; the structure ofω-limit sets, sets of periodic and nonwandering points is described; the topological entropy of elementary maps is shown to be equal to 0. Examples are given illustrating the differences in the entropic properties of continuous maps of dendrites with a countable set of branch points and continuous maps of their retracts which are finite trees. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 183–195, February, 1998. This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01755. |
