On quantitative estimates for quasiintegral points in orbits of semigroups of rational maps (Q2329091)

The author generalizes the results of the paper of \textit{L.-C. Hsia} and \textit{J. H. Silverman} [Pac. J. Math. 249, No. 2, 321--342 (2011; Zbl 1272.37039)]. The introductory section contains a list of previous results and the motivation. Important facts about height functions, distance and dynamics on the projective line are discussed in the next two sections. A quantitative version of Roth's theorem and some known facts about the index of ramification are stated in Section 4. The main theorem determining a bound for the number of quasi-integral points on a given orbit is proved in the final section.