Dynamics of piecewise linear maps and sets of nonnegative matrices I . Bondarenko December 2 , 2008

Abstract

We consider functions fv = minA∈KAv and gv = maxA∈KAv, where K is a finite set of nonnegative matrices and by “min” and “max” we mean coordinatewise minimum and maximum. We transfer known results about properties of g to f . In particular we show existence of nonnegative generalized eigenvectors for f , give necessary and sufficient conditions for existence of strictly positive eigenvector for f , study dynamics of f on the positive cone. We show the existence and construct matrices A and B, possibly not in K, such that fv ∼ Av and gv ∼ Bv for any strictly positive vector v.

Cite this paper

@inproceedings{Bondarenko2008DynamicsOP, title={Dynamics of piecewise linear maps and sets of nonnegative matrices I . Bondarenko December 2 , 2008}, author={I. Bondarenko}, year={2008} }