Abstract
We consider two commuting automorphismsT 1,T 2 of the Lebesque space (M, M, μ) such thath m,n=h(T m1 T n2 )<∞ whereh is the measure-theoretic entropy. Under additional assumptions we show the existence of the limits lim (1/m)h m,n wherem→∞,n→∞,m/n→ω and ω is an irrational number.
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Sinai, Y.G. An answer to a question by J. Milnor. Commentarii Mathematici Helvetici 60, 173–178 (1985). https://doi.org/10.1007/BF02567408
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DOI: https://doi.org/10.1007/BF02567408