A Study of the Dynamics of the Family f λ ,μ = λsinz+μ/(z−kπ) where λ ,μ ∈ R\{0} and k ∈ Z\{0} - Domínguez, Patricia; Vázquez, Josué; Oca, Marco A. Montes de (Discontinuity, Nonlinearity, and Complexity, 2026)
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.