The cycle time vector of D-A-D functions

It is of interest to find conditions under which the cycle time vector, View the MathML source, of a topical function F, that is a function from View the MathML source into itself which is homogeneous and nonexpansive in the View the MathML source norm, exists. For a class of topical functions associated with matrix scaling problems, we show that the cycle time vector exists and that it can be computed from the spectral radius of the function.