Postcritically Finite Maps
Dimension 1, degree 2 polynomials over quadratic fields
A map is postcritically finite (PCF) if every critical point has a finite forward orbit. Its critical portrait is the graph of the critical points and their forward orbits. Critical points are counted over the algebraic closure, including ∞ for polynomials.
Functions over quadratic fields: 1 conjugacy class over Export to Sage
| Label | Function | Field of Definition | Critical Points | Critical Point Field | Portrait Size | Portrait Cycles | Portrait Components | Portrait | Citations |
|---|---|---|---|---|---|---|---|---|---|
| 1.e9464d8c.638cd9c2.1 | (x2 + ay2 : y2) | 2.0.4.1 | 2 | 2.0.4.1 | 5 | 2, 1 | 4, 1 | view | Doyle2014, Doyle2018, Doyle2020 |