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Characterizations of intrinsically random dynamical systems

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  • Suchanecki, Zdzisław
  • Weron, Aleksander

Abstract

We show that intrinsically random dynamical systems with the Prigogine operator Λ of the form of a random Laplace transform, can be characterized as Kolmogorov flows (K-flows). We also obtain a spectral characterization in the language of the Weyl commutation relation. As a consequence we conclude that the dynamical system is intrinsically random if and only if its Liouvillian and time operators form a Schrödinger couple.

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  • Suchanecki, Zdzisław & Weron, Aleksander, 1990. "Characterizations of intrinsically random dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 166(2), pages 220-228.
    • Handle: RePEc:eee:phsmap:v:166:y:1990:i:2:p:220-228
    DOI: 10.1016/0378-4371(90)90014-J
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    1. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
    2. Rybaczuk, M. & Weron, K., 1989. "Linearly coupled quantum oscillators with Lévy stable noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 519-526.
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    1. Suchanecki, Zdzislaw, 1992. "On lambda and internal time operators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(1), pages 249-266.

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