An answer to a question by J. Milnor

Ya G. Sinai

doi:10.1007/BF02567408

An answer to a question by J. Milnor

Ya G. Sinai

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Abstract

We consider two commuting automorphisms T₁, T₂ of the Lebesque space (M, M, μ) such that h_m,n=h(T₁^m T₂ⁿ )<∞ 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 language	English (US)
Pages (from-to)	173-178
Number of pages	6
Journal	Commentarii Mathematici Helvetici
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/BF02567408
State	Published - Dec 1985

All Science Journal Classification (ASJC) codes

General Mathematics

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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.",

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N2 - 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.

AB - 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.

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JO - Commentarii Mathematici Helvetici

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An answer to a question by J. Milnor

Abstract

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