-
Abstract
We consider a map called a double rotation,
which is composed of two rotations on a circle.
Specifically, a double rotation is a map on the interval $[0,1)$
that maps $x\in[0,c)$ to $\{x+\alpha\}$, and $x\in[c,1)$ to $\{x+\beta\}$.
Although double rotations are discontinuous and noninvertible in general,
we show that almost every double rotation can be
reduced to a simple rotation,
and the set of the parameter values such that the double rotation is
irreducible to a rotation has a fractal structure.
We also examine a characteristic number of a double rotation,
which is called a discharge number.
The graph of the discharge number as a function of $c$
reflects the fractal structure, and is very complicated.
Mathematics Subject Classification: 37E05, 37E10, 37B05.
\begin{equation} \\ \end{equation}
-
Access History
-
{{journal.titleEn}} 
DownLoad: