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A note on Markov operators and transition systems

Tom 91 / 2002

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

Streszczenie

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.

Autorzy

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

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