The backward continued fraction map and geodesic flow
نویسندگان
چکیده
منابع مشابه
Geodesic laminations and continued fractions
We introduce the notion of “slope” for geodesic laminations. Slope is a positive irrational defined via regular continued fraction. The action of the mapping class group on lamination pulls back to the action of GL(2, Z) on real line. We discuss applications of slopes in complex analysis, low-dimensional topology, geometric group theory and C∗-algebras.
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We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
متن کاملThe Hurwitz Complex Continued Fraction
The Hurwitz complex continued fraction algorithm generates Gaussian rational approximations to an arbitrary complex number α by way of a sequence (a0, a1, . . .) of Gaussian integers determined by a0 = [α], z0 = α − a0, (where [u] denotes the Gaussian integer nearest u) and for j ≥ 1, aj = [1/zj−1], zj = 1/zj−1−aj . The rational approximations are the finite continued fractions [a0; a1, . . . ,...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1984
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700002583