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An answer to a question by J. Milnor |
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| Authors: | Ya G Sinai |
| Institution: | (1) L. D. Landau Institute of Theoretical Physics, Academy of Sciences of USSR, Moscow, USSR |
| Abstract: | We consider two commuting automorphismsT 1,T 2 of the Lebesque space (M, M, μ) such thath m,n=h(T 1 m T 2 n )<∞ 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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