Open AccessOn the spherical derivative of a rational function
Author(s) -
Matthew Barrett,
Alexandre Erëmenko
Publication year - 2014
Publication title -
analysis and mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.456
H-Index - 16
eISSN - 1664-235X
pISSN - 1664-2368
DOI - 10.1007/s13324-014-0071-3
Subject(s) - infimum and supremum , uniform norm , mathematics , norm (philosophy) , iterated function , function (biology) , derivative (finance) , rational function , pure mathematics , metric (unit) , second derivative , mathematical analysis , combinatorics , economics , operations management , evolutionary biology , political science , financial economics , law , biology
For a rational function \(f\) we consider the norm of the derivative with respect to the spherical metric and denote by \(K(f)\) the supremum of this norm. We give estimates of this quantity \(K(f)\) both for an individual function and for sequences of iterates.
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