Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 21, No. 2, pp. 113-125 (2005)

Continued Fractions and the Gauss Map

Bruce Bates, Martin Bunder and Keith Tognetti

University of Wollongong

Abstract: We discover properties of the Gauss Map and its iterates using continued fractions. In particular, we find all fixed points and show that the graph of an iterate over [0,1/2] is symmetric to the graph of the next higher iterate over [1/2,1].

Keywords: Continued fractions, Gauss Map

Classification (MSC2000): 11A55; 37E05

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