We find all quadratic post-critically finite (PCF) rational functions defined over Q , up to conjugation by elements of PGL₂(Q̄) . We describe an algorithm to search for possibly PCF functions. Using the algorithm, we eliminate all but 12 rational functions, all of which are verified to be PCF. We also give a complete description of all possible rational preperiodic structures for quadratic PCF functions defined over Q .
No takes yet. Share an insight, caveat, or question.
Lukas et al. (2014) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: