A note on Markov operators and transition systems

• Autorzy: Bartosz Frej
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 37B50: Multi-dimensional shifts of finite type, tiling dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 91
• Numer: 2
• Strony: 183-190

Daty

wydano

2002

Twórcy

autor

Bartosz Frej

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm91-2-3