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On Sets Where Iterates of a Meromorphic Function Zip Towards Infinity
Author(s) -
Rippon P. J.,
Stallard G. M.
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930000730x
Subject(s) - meromorphic function , mathematics , infinity , iterated function , function (biology) , pure mathematics , l function , mathematical analysis , evolutionary biology , biology
For a transcendental meromorphic function f , various properties of the set [formula] were obtained in [ 8 ] and [ 9 ]. Here we establish analogous properties for the smaller sets [formula] introduced in [ 5 ], and [formula] We deduce a symmetry result for Julia sets J ( f ), and also indicate some techniques for showing that certain invariant curves lie in I ′( f ), Z ( f ) and J ( f ). 2000 Mathematics Subject Classification 30D05, 37F10, 37F50.