Asymptotic orbit complexity of infinite measure preserving transformations

February 2006, 15(1): 353-366. doi: 10.3934/dcds.2006.15.353

Asymptotic orbit complexity of infinite measure preserving transformations

1.	Faculty of Mathematics, University of Vienna, Nordbergstraβe 15, 1090 Vienna, Austria

Received December 2004 Revised September 2005 Published February 2006

Abstract
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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.

Keywords: Kolmogorov complexity, inﬁnite invariant measure, indifferent orbits, algorithmic information content, ratio ergodic theorem., intermittency.

Mathematics Subject Classification: Primary: 37A40, 03D15; Secondary: 37A35, 37E0.

Citation: Roland Zweimüller. Asymptotic orbit complexity of infinite measure preserving transformations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 353-366. doi: 10.3934/dcds.2006.15.353

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