Iteration of a quaternionic quadratic family (Q1924301)

Since multiplication of quaternions is not commutative, a quadratic function in quaternions reads \[ q(X)=\sum_i F_iX G_iX H_i+\sum_j J_jXK_j+C. \] Contrary to the complex case, this form cannot be reduced to a one-parameter case \(g_Q(X)=X^2+Q\). In the paper the quadratic families \(f_\Lambda=\Lambda X(1-X)\) and \(h_\Theta= \Theta X^2+1\) are considered. Although they have many common properties, they are not linearly conjugate unless \(\Lambda\) and \(\Theta\) are real.