Asymptotic orbit complexity of infinite measure preserving transformations
Roland Zweimüller
Discrete & Continuous Dynamical Systems - A 2006, 15(1): 353-366 doi: 10.3934/dcds.2006.15.353
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
Invariant measures for general induced maps and towers
Arno Berger Roland Zweimüller
Discrete & Continuous Dynamical Systems - A 2013, 33(9): 3885-3901 doi: 10.3934/dcds.2013.33.3885
Absolutely continuous invariant measures (acims) for general induced transformations are shown to be related, in a natural way, to popular tower constructions regardless of any particulars of the latter. When combined with (an appropriate generalization of) the known integrability criterion for the existence of such acims, this leads to necessary and sufficient conditions under which acims can be lifted to, or projected from, nonsingular extensions.
keywords: jump transformation Hofbauer tower Young tower infinite ergodic theory. Markov extension Induced transformation

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