# Quadratic rational functions with a periodic critical point

Seminar

Speaker

Dr. Solomon Vishkautsan (Scuola Normale Superiore di Pisa)

Date

30/12/2015 - 11:30 - 10:30Add to Calendar

`2015-12-30 10:30:00``2015-12-30 11:30:00``Quadratic rational functions with a periodic critical point``A rational function defined over the rationals has only finitely many rational preperiodic points by Northcott's classical theorem. These points describe a finite directed graph (with arrows connecting between each preperiodic point and its image under the function). We give a classification, up to a conjecture, of all possible graphs of quadratic rational functions with a rational periodic critical point. This generalizes the classification of such graphs for quadratic polynomials over the rationals by Poonen (1998). This is a joint work with Jung Kyu Canci (Universität Basel).``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room

Abstract

A rational function defined over the rationals has only finitely many rational preperiodic points by Northcott's classical theorem. These points describe a finite directed graph (with arrows connecting between each preperiodic point and its image under the function). We give a classification, up to a conjecture, of all possible graphs of quadratic rational functions with a rational periodic critical point. This generalizes the classification of such graphs for quadratic polynomials over the rationals by Poonen (1998). This is a joint work with Jung Kyu Canci (Universität Basel).

Last Updated Date : 24/12/2015