On the entropy of Japanese continued fractions
| dc.creator | Luzzi, Laura | |
| dc.creator | Marmi, Stefano | |
| dc.date | 2006-01-24 | |
| dc.date | 2006-06-01 | |
| dc.date.accessioned | 2026-07-07T06:59:14Z | |
| dc.date.available | 2026-07-07T06:59:14Z | |
| dc.description | We consider a one-parameter family of expanding interval maps $\{T_α\}_{α\in [0,1]}$ (japanese continued fractions) which include the Gauss map ($α=1$) and the nearest integer and by-excess continued fraction maps ($α={1/2},α=0$). We prove that the Kolmogorov-Sinai entropy $h(α)$ of these maps depends continuously on the parameter and that $h(α) \to 0$ as $α\to 0$. 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 $T_α$ for $α=\frac{1}{n}$. | |
| dc.description | 42 pages, 12 figures; v2: minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0601576 | |
| dc.identifier | http://arxiv.org/abs/math/0601576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107672 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Number Theory | |
| dc.subject | 11K50 (Primary) 37A10, 37A35, 37E05 (Secondary) | |
| dc.title | On the entropy of Japanese continued fractions | |
| dc.type | text |