### Abstract:

In the field of arithmetic dynamics, we are interested in classifying points in a number field K depending on their orbit, that is, how they behave under repeated application of a given rational function $f$. Recently, Ostafe, Pottymeyer and Shparlinski have given a classification of points whose orbits generated by a given polynomial contain perfect powers. This talk will provide an effective background to understand these results and will then give a generalisation for this work which focuses on powers in the orbits of rational functions.

Speaker