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In this paper, we have investigated the Bungee set of composition of twotranscendental entire functions. We have provided a class of permutable entirefunctions for which their Bungee sets are equal. Moreover, we have obtained aresult on permutable entire functions for which the escaping set of thecomposite entire function equals the union of the escaping sets of the twofunctions. In addition, we establish important relations between the Bungeeset, Escaping set and Filled Julia set of composite entire functions with thatof its individual functions.

Dynamics on Bungee set, Escaping set and Filled Julia set of Composite Transcendental Entire Functions