Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class
Abstract
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 some relation between the dynamics of composition of entire functions and the functions taken for composition. We have shown that the union of the bungee set of two entire functions contains the bungee set of the composite function. In addition, it is shown that the filled-in Julia set of composite entire functions contains the filled-in Julia set of functions used for the composition. The results have been illustrated with several examples. We have mostly dealt with permutable(commuting) functions.
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