, Volume 134, Issue 2, pp 121-141

Entropy Theory from the Orbital Point of View

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Abstract.

 Inspired by [17], we develop an orbital approach to the entropy theory for actions of countable amenable groups. This is applied to extend – with new short proofs – the recent results about uniform mixing of actions with completely positive entropy [17], Pinsker factors and the relative disjointness problems [10], Abramov–Rokhlin entropy addition formula [19], etc. Unlike the cited papers our work is independent of the standard machinery developed by Ornstein–Weiss [14] or Kieffer [12]. We do not use non-orbital tools like the Rokhlin lemma, the Shannon–McMillan theorem, castle analysis, joining techniques for amenable actions, etc. which play an essential role in [17], [19] and [10].

(Received 23 October 2000)