A Study of the Dynamics of the Family f λ ,μ = λsinz+μ/(z−kπ) where λ ,μ ∈ R\{0} and k ∈ Z\{0}

Patricia Domínguez; Josué Vázquez; Marco A. Montes de Oca

Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

A Study of the Dynamics of the Family f λ ,μ = λsinz+μ/(z−kπ) where λ ,μ ∈ R\{0} and k ∈ Z\{0}

Discontinuity, Nonlinearity, and Complexity 5(4) (2016) 407--414 | DOI:10.5890/DNC.2016.12.006

Patricia Domínguez; Josué Vázquez; Marco A. Montes de Oca

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, Pue. CP. 72595, Mexico

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Abstract

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.

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