Continued Fractions and Chaos
Continued fractions also play a role in the study of chaos, where they tie together the 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 called the Gauss map, which lops off digits of a continued fraction expansion: . 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.
Read more about this topic: Continued Fraction
Famous quotes containing the words continued and/or chaos:
“Madame, all stories, if continued far enough, end in death, and he is no true-story teller who would keep that from you.”
—Ernest Hemingway (1899–1961)
“She comes! She comes! The sable throne behold
Of Night primaeval, and of Chaos old!”
—Alexander Pope (1688–1744)