Eur. Phys. J. Spec. Top.
https://doi.org/10.1140/epjs/s11734-025-01583-2

Regular Article

Dynamics of meromorphic functions involving cosine

Department of Mathematics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam, India

^a mgpp@iitg.ac.in

Received: 13 December 2024
Accepted: 14 March 2025
Published online: 11 April 2025

Abstract

In the theory of dynamical systems, attractors represent states toward which a system tends to evolve. The basins of attraction are the regions of initial conditions leading to a particular attractor. In this paper, a single parameter family of even meromorphic functions $f_{\lambda }$ involving cosine function for $\lambda >0$, is considered. The dynamics of functions $f_{\lambda }$ is investigated. Also, it is shown that there exists ${\lambda }^{\ast }>0$ such that the Fatou set (or stable set) of $f_{\lambda }$ is the basin of attraction of an attracting fixed point and the Julia set (or the set of chaotic points) of $f_{\lambda }$ is disconnected for $\lambda >{\lambda }^{\ast }$.