## 抄録

We consider the α-continued fraction transformations T _{α}, 0 < α ≤ 1, the one parameter family of one-dimensional maps. Recently, Luzzi and Marmi showed that the entropy of T_{α} varies continuously as α varies and tends to zero as α tends to zero. They also observed by computer simulation that the entropy is not monotone as a function of α. In this paper, we first give an estimate of the decay rate of the entropy as α tends to zero. Then we show that there exist decreasing sequences of intervals of α, (I _{n}), (J_{n}), (K_{n}), (L_{n}) such that (a) 1/n, (b) I_{n+1} < J_{n} < K_{n} < L _{n} < I_{n}, (c) the entropy of T_{α} is increasing on I_{n}, decreasing on K_{n} and constant (depends on n) on J_{n} and L_{n}.

本文言語 | English |
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ページ（範囲） | 1207-1225 |

ページ数 | 19 |

ジャーナル | Nonlinearity |

巻 | 21 |

号 | 6 |

DOI | |

出版ステータス | Published - 2008 6月 1 |

## ASJC Scopus subject areas

- 統計物理学および非線形物理学
- 数理物理学
- 物理学および天文学（全般）
- 応用数学