Dynamics of the Modified Chebyshev's method to multiple roots

This study explores the complex dynamics of the rational function associated with the Modified Chebyshev's root-finding method. After introducing the basic preliminaries of discrete dynamical systems, we analyze the dynamical behavior of the method, classifying the stability of its fixed points and critical orbits. These theoretical findings are then illustrated through dynamical planes, which map the basins of attraction and reveal the convergence characteristics and potential chaotic regions of the method.