Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields (Q1715021)

The author studies the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields. He gives a detailed description of the structure of their graphs, finding that they are formed by a finite number of connected components, each component consisting of a cycle, whose vertices are roots of reversed trees. In the end three different elliptic curves and endomorphisms are chosen in order to illustrate the ideas. This work generalizes previous works of the author in an unified frame.