## Journals

- Advances in Mathematics of Communications
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DCDS

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.

DCDS

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.

## Year of publication

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