\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On the entropy of Japanese continued fractions

Abstract Related Papers Cited by
  • We consider a one-parameter family of expanding interval maps $\{T_{\alpha}\}_{\alpha \in [0,1]}$ (Japanese continued fractions) which include the Gauss map ($\alpha=1$) and the nearest integer and by-excess continued fraction maps ($\alpha=\frac{1}{2},\,\alpha=0$). We prove that the Kolmogorov-Sinai entropy $h(\alpha)$ of these maps depends continuously on the parameter and that $h(\alpha) \to 0$ as $\alpha \to 0$. Numerical results suggest that this convergence is not monotone and that the entropy function has infinitely many phase transitions and a self-similar structure. Finally, we find the natural extension and the invariant densities of the maps $T_{\alpha}$ for $\alpha=\frac{1}{n}$.
    Mathematics Subject Classification: Primary: 11K50; Secondary: 37A10, 37A35, 37E05.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(94) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return