On a compact metric space X one defines a transition system to be a lower semicontinuous map . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-3,
author = {Bartosz Frej},
title = {A note on Markov operators and transition systems},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {183-190},
zbl = {1115.37304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-3}
}
Bartosz Frej. A note on Markov operators and transition systems. Colloquium Mathematicae, Tome 91 (2002) pp. 183-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-3/