In a recent breakthrough, Dimitrov solved the Schinzel-Zassenhaus Conjecture. We follow his approach and adapt it to certain dynamical systems arising from polynomials of the form Tp+c where p is a prime number and where the orbit of 0 is finite. For example, if p=2
Nearby in the stack
, and
0
is periodic under
T2+c
with
c∈R∖{−2}
, we prove a lower bound for the local canonical height of a wandering algebraic integer that is inversely proportional to the field degree. From this we are able to deduce a lower bound for the canonical height of a wandering point that decays like the inverse square of the field degree.