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In this article, the real dynamics of the one-parameter family of meromorphic functions \(f_{\lambda }(z) = \lambda \Big (1+\frac{1}{z} \Big )\cosh {z}\) for \(z \in \mathbb {C}\) , where \(\lambda \) is a positive real number, is studied, and its singular values are explored. It is discovered that \(f_{\lambda }\) possesses an infinite number of singular values, yet they remain bounded within the complex plane. Finally, some inferences are given on the complex dynamics of \(f_{\lambda }\) .

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Dynamics of \(f_{\lambda }(z) = \displaystyle \lambda \left( 1+\frac{1}{z} \right) {\cosh z}\) and Its Singularities

  • 会议论文

  • 发表日期：

    2025年

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  • Gaurav Kumar,
  • Sudip Kumar,
  • M. Guru Prem Prasad

摘要

In this article, the real dynamics of the one-parameter family of meromorphic functions \(f_{\lambda }(z) = \lambda \Big (1+\frac{1}{z} \Big )\cosh {z}\) for \(z \in \mathbb {C}\) , where \(\lambda \) is a positive real number, is studied, and its singular values are explored. It is discovered that \(f_{\lambda }\) possesses an infinite number of singular values, yet they remain bounded within the complex plane. Finally, some inferences are given on the complex dynamics of \(f_{\lambda }\) .