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

Dinesh Kumar, Soumyajeet Das

Published 2024-05-18Version 1

In this paper, we have discussed the dynamics of composite entire functions in terms of relationship between Bungee set and repelling periodic points(to be denoted by $RP$. We have established relation between the dynamics of composite function and the functions taken for composition. We showed that the union of their Bungee sets contains Bungee set of the composite function. We also showed that $RP$ set of composite functions contains the $ RP$ set of functions used for the composition. We have mostly dealt with the functions of class $\mathcal{B}$ which are also permutable. These results hold true when we have a composite function in which one function is a periodic translation of another.