Mathematics

A polynomial map is called post-critically finite (PCF) if all of its critical orbits are finite(i.e, all critical points are preperiodic). In this talk, I will discuss a finiteness result of totally real PCF parameters of a quadratic polynomial. This is joint work (in progress) with Clay Petsche. Our technique relies upon the dynamical and potential-theoretical features of the Mandelbrot set and algebraic properties of a monic Jacobi polynomial.