### 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 language | English (US) |
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Pages (from-to) | 173-178 |

Number of pages | 6 |

Journal | Commentarii Mathematici Helvetici |

Volume | 60 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1985 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Sinai, Y. G. (1985). An answer to a question by J. Milnor.

*Commentarii Mathematici Helvetici*,*60*(1), 173-178. https://doi.org/10.1007/BF02567408