Asymptotic orbit complexity of infinite measure preserving transformations

Roland Zweimüller

doi:10.3934/dcds.2006.15.353

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2006, Volume 15, Issue 1: 353-366. Doi: 10.3934/dcds.2006.15.353

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Asymptotic orbit complexity of infinite measure preserving transformations

Roland Zweimüller^1,

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

Received: December 2004

Revised: September 2005

Published: March 2006

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Abstract

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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Mathematics Subject Classification: Primary: 37A40, 03D15; Secondary: 37A35, 37E05.

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