Dinesh Kumar

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20242026

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math.DS2026

A survey on permutable transcendental entire functions and their dynamics

Dinesh Kumar

In this paper, we survey important results on the dynamics of permutable transcendental entire functions from 1958 to 2025. We have discussed the forms of transcendental entire fun…

math.DS2026

Results on the postsingular set of compositions of transcendental entire functions

Manisha Kumari, Dinesh Kumar

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$ , where $g = a f^{p} + b$ with $a, b \in C$ , $p \in N$ , and $a \neq = 0, 1$ . We exami…

math.DS2026

Equality of the dynamical sets of two commuting transcendental entire functions

Manisha Kumari, Dinesh Kumar

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$ , where $g$ is of the form $a f^{p} + b$ with $a,b \in \C$, $p \in N$ , and $a \neq = 0, 1$ .…

math.DS2025

Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class

Dinesh Kumar, Soumyajeet Das

In this paper, we have discussed the dynamics of composite entire functions in terms of relationship between bungee set, escaping set and filled-in Julia set. We have established s…

math.DS2025

On Dynamics of the Bungee set and the Filled Julia set of a Transcendental Semigroup

Manisha Kumari, Dinesh Kumar

We have introduced the notion of the bungee set and the filled Julia set of a transcendental semigroup using Fatou-Julia theory. Numerous results of the bungee set of a single tran…