LEADER 03878nam 2200733Ia 450 001 9910823642103321 005 20200520144314.0 010 $a1-107-16900-3 010 $a1-280-81565-5 010 $a9786610815654 010 $a0-511-27476-9 010 $a0-511-27546-3 010 $a0-511-27321-5 010 $a0-511-32145-7 010 $a0-511-61878-6 010 $a0-511-27400-9 035 $a(CKB)1000000000352103 035 $a(EBL)288630 035 $a(OCoLC)162145460 035 $a(SSID)ssj0000175583 035 $a(PQKBManifestationID)11165624 035 $a(PQKBTitleCode)TC0000175583 035 $a(PQKBWorkID)10190463 035 $a(PQKB)10565798 035 $a(UkCbUP)CR9780511618789 035 $a(Au-PeEL)EBL288630 035 $a(CaPaEBR)ebr10171412 035 $a(CaONFJC)MIL81565 035 $a(MiAaPQ)EBC288630 035 $a(PPN)145854108 035 $a(EXLCZ)991000000000352103 100 $a20060927d2007 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHyperbolic geometry from a local viewpoint /$fLinda Keen and Nikola Lakic 205 $a1st ed. 210 $aCambridge $cCambridge University Press$d2007 215 $a1 online resource (x, 271 pages) $cdigital, PDF file(s) 225 1 $aLondon Mathematical Society student texts ;$v68 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-68224-X 311 $a0-521-86360-0 320 $aIncludes bibliographical references and index. 327 $aCover; Series-title; Title; Copyright; Dedication; Contents; Introduction; 1 Elementary transformations of the Euclidean plane and the Riemann sphere; 2 Hyperbolic metric in the unit disk; 3 Holomorphic functions; 4 Topology and uniformization; 5 Discontinuous groups; 6 Fuchsian groups; 7 The hyperbolic metric for arbitrary domains; 8 The Kobayashi metric; 9 The Carathe?odory pseudo-metric; 10 Inclusion mappings and contraction properties; 11 Applications I: forward random holomorphic iteration; 12 Applications II: backward random iteration; 13 Applications III: limit functions 327 $a14 Estimating hyperbolic densities15 Uniformly perfect domains; 16 Appendix: a brief survey of elliptic functions; Bibliography; Index 330 $aWritten for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems. 410 0$aLondon Mathematical Society student texts ;$v68. 606 $aGeometry, Hyperbolic 606 $aGeometry, Non-Euclidean 615 0$aGeometry, Hyperbolic. 615 0$aGeometry, Non-Euclidean. 676 $a516.9 700 $aKeen$b Linda$057201 701 $aLakic$b Nikola$f1966-$067027 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910823642103321 996 $aHyperbolic geometry from a local viewpoint$94190556 997 $aUNINA