We consider an optimal fourth-order method for solving nonlinear equations and construct polynomials such that the rational map arising from the method applied to these polynomials has an attracting periodic orbit of any prescribed period.
"Attracting Periodic Cycles for an Optimal Fourth-Order Nonlinear Solver." Abstr. Appl. Anal. 2012 (SI12) 1 - 8, 2012. https://doi.org/10.1155/2012/263893