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Properties of differences of meromorphic functions

Zong-Xuan Chen, Kwang Ho Shon (2011)

Czechoslovak Mathematical Journal

Let f be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference g ( z ) = f ( z + c ) - f ( z ) and the divided difference g ( z ) / f ( z ) .

Pseudo-iteration semigroups and commuting holomorphic maps

Graziano Gentili, Fabio Vlacci (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A connection between iteration theory and the study of sets of commuting holomorphic maps is investigated, in the unit disc of C . In particular, given two holomorphic maps f and g of the unit disc into itself, it is proved that if g belongs to the pseudo-iteration semigroup of f (in the sense of Cowen) then - under certain conditions on the behaviour of their iterates - the maps f and g commute.

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