Editing Simple continued fraction (section)

===Dynamical systems===
Continued fractions also play a role in the study of [[dynamical system]]s, where they tie together the [[Farey sequence|Farey fractions]] which are seen in the [[Mandelbrot set]] with [[Minkowski's question-mark function]] and the [[modular group]] Gamma.

The backwards [[shift operator]] for continued fractions is the map {{math|''h''(''x'') {{=}} 1/{{mvar|x}} − ⌊1/{{mvar|x}}⌋}} called the '''[[Gauss–Kuzmin–Wirsing operator|Gauss map]]''', which lops off digits of a continued fraction expansion: {{math|''h''([0; ''a''{{sub|1}}, ''a''{{sub|2}}, ''a''{{sub|3}}, ...]) {{=}} [0; ''a''{{sub|2}}, ''a''{{sub|3}}, ...]}}. The [[transfer operator]] of this map is called the [[Gauss–Kuzmin–Wirsing operator]]. The distribution of the digits in continued fractions is given by the zero'th [[eigenvector]] of this operator, and is called the [[Gauss–Kuzmin distribution]].