Geodesic
Continuous extension of order-preserving homogeneous maps
Kybernetika, Tome 39 (2003) no. 2, p. [205].

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Maps $f$ defined on the interior of the standard non-negative cone $K$ in ${\mathbb{R}}^N$ which are both homogeneous of degree $1$ and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least one eigenvector in $K-\lbrace 0\rbrace $. In the case where the cycle time $\chi (f)$ of the original map does not exist, such eigenvectors must lie in $\partial {K}-\lbrace 0\rbrace $.
Classification : 06F05, 47H07, 47N70, 93B27, 93B28, 93C65
Keywords: discrete event systems; order-preserving homogeneous maps 
@article{KYB_2003__39_2_a9,
     author = {Burbanks, Andrew D. and Sparrow, Colin T. and Nussbaum, Roger D.},
     title = {Continuous extension of order-preserving homogeneous maps},
     journal = {Kybernetika},
     pages = {[205]},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2003},
     mrnumber = {1996558},
     zbl = {1249.93123},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a9/}
}
TY  - JOUR
AU  - Burbanks, Andrew D.
AU  - Sparrow, Colin T.
AU  - Nussbaum, Roger D.
TI  - Continuous extension of order-preserving homogeneous maps
JO  - Kybernetika
PY  - 2003
SP  - [205]
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a9/
LA  - en
ID  - KYB_2003__39_2_a9
ER  - 
%0 Journal Article
%A Burbanks, Andrew D.
%A Sparrow, Colin T.
%A Nussbaum, Roger D.
%T Continuous extension of order-preserving homogeneous maps
%J Kybernetika
%D 2003
%P [205]
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a9/
%G en
%F KYB_2003__39_2_a9
Burbanks, Andrew D.; Sparrow, Colin T.; Nussbaum, Roger D. Continuous extension of order-preserving homogeneous maps. Kybernetika, Tome 39 (2003) no. 2, p. [205]. http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a9/