Asymptotic orbit complexity of infinite measure preserving transformations | Zendy

Roland Zweimüller | Zendy

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Asymptotic orbit complexity of infinite measure preserving transformations

Author(s) -

Roland Zweimüller

Publication year - 2006

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2006.15.353

Subject(s) - ergodic theory , measure (data warehouse) , mathematics , stationary ergodic process , orbit (dynamics) , pure mathematics , kolmogorov complexity , discrete mathematics , invariant measure , computer science , database , engineering , aerospace engineering

We determine the asymptotics of the Kolmogorov complexity of symbolic orbits of certain infinite measure preserving transformations. Specifically, we prove that the Brudno - White individual ergodic theorem for the complexity generalizes to a ratio ergodic theorem analogous to previously established extensions of the Shannon - McMillan - Breiman theorem.

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