Sullivan, Dennis Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics. (English) Zbl 0517.58028 Acta Math. 149, 215-237 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 91 Documents MSC: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry 37A99 Ergodic theory 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) 51M10 Hyperbolic and elliptic geometries (general) and generalizations 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 11K60 Diophantine approximation in probabilistic number theory 30B70 Continued fractions; complex-analytic aspects 53C22 Geodesics in global differential geometry Keywords:disjoint circles; imaginary quadratic fields; logarithm law for geodesics; Borel-Cantelli lemma; Khinchin’s approximation theorem; geometrically finite Kleinian group; approximation of rationals PDFBibTeX XMLCite \textit{D. Sullivan}, Acta Math. 149, 215--237 (1982; Zbl 0517.58028) Full Text: DOI References: [1] [R]Rudolf, D. To appear inErgodic Theory and Dynamical Systems, 1982–1983 [2] [AS]Aaronson, J. & Sullivan, D. Preprint Te Aviv University. [3] [Sc]Schmidt, W., A metrical theorem in diophantine approximation.Canad. J. Math., 12 (1960), 619–631. · Zbl 0097.26205 [4] [Sw]Swan, R., Generators and relations for certain linear groups.Adv. in Math., 6 (1971). 1–77. · Zbl 0221.20060 [5] [S1]Sullivan, D., The density at infinity of a discrete group of hyperbolic isometries.I.H.E.S. Publ. Math., 50 (1979), 171–202. · Zbl 0439.30034 [6] [S1]Sullivan, D., Entropy, Hausdort measures old and new, and limit sets of geometrically finite Kleninian groups. Submitted toActa Math., Feb. 1981. [7] [T]Thurstron, B.,Geometry and topology of 3-manifolds. Princeton notes, 1978. [8] [ASc]Schmidt, A. L., Diophantine approximation of complex numbers.Acta Math., 134 (1975), 1–84 · Zbl 0329.10023 [9] [L]LeVeque, W. J., Continued fractions and approximations I and IIIndag. Math., 14 (1952), 526–545. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.