Results on escaping set of an entire function and its composition

Ramanpreet Kaur () and Dinesh Kumar ()
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Ramanpreet Kaur: University of Delhi
Dinesh Kumar: Deen Dayal Upadhyaya College, University of Delhi

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 79-86

Abstract: Abstract Given two permutable entire functions f and g, we establish vital relationship between escaping sets of entire functions f, g and their composition. We provide some families of transcendental entire functions for which Eremenko’s conjecture holds. In addition, we investigate the dynamical properties of the mapping $$f(z)=z+1+e^{-z}.$$ f ( z ) = z + 1 + e - z .

Keywords: Escaping set; Normal family; Postsingular set; Postsingularly bounded; Hyperbolic; 37F10; 30D05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00121-9

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