The non-monotonicity of the entropy of α-continued fraction transformations

Hitoshi Nakada, Rie Natsui

研究成果: Article査読

22 被引用数 (Scopus)

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 Tα 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), (Jn), (Kn), (Ln) such that (a) 1/n, (b) In+1 < Jn < Kn < L n < In, (c) the entropy of Tα is increasing on In, decreasing on Kn and constant (depends on n) on Jn and Ln.

本文言語English
ページ(範囲)1207-1225
ページ数19
ジャーナルNonlinearity
21
6
DOI
出版ステータスPublished - 2008 6 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

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