A+ CATEGORY SCIENTIFIC UNIT

A note on Markov operators and transition systems

Volume 91 / 2002

Bartosz Frej Colloquium Mathematicum 91 (2002), 183-190 MSC: 37A30, 37B50. DOI: 10.4064/cm91-2-3

Abstract

On a compact metric space $X$ one defines a transition system to be a lower semicontinuous map $X\to 2^X$. 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.

Authors

  • Bartosz FrejInstitute of Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image