Dynamik von Polynomen in Kreisebenen (Q1312690)

The complex plane is obtained from the real numbers by adjoining a non- real number \(i\) satisfying \(i^ 2=-1\). The Minkowski plane and Laguerre plane are obtained by adjoining non-real elements \(j\) and \(e\) satisfying \(j^ 2=1\) and \(e^ 2=0\), respectively. The iteration theory of polynomials over the complex numbers has received much attention in recent years. In this paper, the iterates \(p_ n\) of a polynomial \(p\) with real coefficients and variable in the Minkowski or Laguerre plane are considered. We quote only one typical result for the Minkowski plane (Satz 2): if the sequence \(p_ n(z)\) is bounded in the real interval \([s,t]\), then it is bounded in the square with diagonal \([s,t]\).