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M. Guru Prem Prasad

Guwahati - 781 039, Assam, India
Department of Mathematics, Indian Institute of Technology, Guwahati


Guru Prem Prasad M.
Chaotic burst in the dynamics of $f_\lambda (z) = \lambda \frac{\sinh (z)}{z}$
2005, vol. 10, no. 1, pp.  71-80
In this paper, a one-parameter family of non-critically finite entire functions $\mathscr{F} \equiv \{f_\lambda(z)=\lambda f(z): \lambda \in \mathbb{R} \setminus \{0\}\}$ with $f(z) = \frac{\sinh z}{z}$ is considered and the dynamics of the entire transcendental functions $f_\lambda \in \mathscr{F}$ is studied in detail. It is shown that there exists a parameter value $\lambda^* > 0$ such that the Julia set of $f_\lambda (z)$ is nowhere dense subset for $0 < |\lambda| \leqslant \lambda^* (\approx 1.104)$. For $|\lambda| > \lambda^*$ the set explodes and becomes equal to the extended complex plane. This phenomenon is referred to as a chaotic burst in the dynamics of the functions $f_\lambda$ in the one-parameter family $\mathscr{F}$.
Keywords: Fatou sets, Julia sets and Chaotic Burst
Citation: Guru Prem Prasad M.,  Chaotic burst in the dynamics of $f_\lambda (z) = \lambda \frac{\sinh (z)}{z}$ , Regular and Chaotic Dynamics, 2005, vol. 10, no. 1, pp. 71-80

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