A Study of the Dynamics of the Family f λ ,μ = λsinz+μ/(z−kπ) where λ ,μ ∈ R{0 and k ∈ Z{0, volume=5, url=https://lhscientificpublishing.com/index.php/DNC/article/view/1955, DOI=10.5890/DNC.2016.12.006, abstractNote=In this article we investigate the dynamics of the meromorphic family f λ ,μ (z) = λ sin z+ μ/( z−kπ) , λ ,μ ∈ R 0 and k ∈ Z 0. We show that for some parameters λ ,μ the Stable set contains an attracting component which is multiply connected and completely invariant. We give a definition of a cut of the space of parameters, with μ and kπ fixed, and show examples of a cut and the Stable and Chaotic sets related to the cut, for some λ given., number=4, journal=Discontinuity, Nonlinearity, and Complexity, author=Domínguez, Patricia and Vázquez, Josué and Oca, Marco A. Montes de, year=2026, month=Aug., pages=407–414