An answer to a question by J. Milnor

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Abstract

We consider two commuting automorphisms T 1, T 2 of the Lebesque space (M, M, μ) such that h m,n=h(T 1 m T 2 n )<∞ where h is the measure-theoretic entropy. Under additional assumptions we show the existence of the limits lim (1/m)h m,n where m→∞, n→∞, m/n→ω and ω is an irrational number.

Original languageEnglish (US)
Pages (from-to)173-178
Number of pages6
JournalCommentarii Mathematici Helvetici
Volume60
Issue number1
DOIs
StatePublished - Dec 1 1985
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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