LEADER 04583nam 22007095 450 001 996418254503316 005 20200701221321.0 010 $a3-030-36782-7 024 7 $a10.1007/978-3-030-36782-4 035 $a(CKB)4100000010327856 035 $a(DE-He213)978-3-030-36782-4 035 $a(MiAaPQ)EBC6109978 035 $a(PPN)242979335 035 $a(EXLCZ)994100000010327856 100 $a20200214d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aContinuous Semigroups of Holomorphic Self-maps of the Unit Disc$b[electronic resource] /$fby Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XXVII, 566 p. 18 illus.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 311 $a3-030-36781-9 327 $aPart I: Preliminaries -- 1 Hyperbolic geometry and interation -- 2. Holomorphic functions with non-negative real part -- 3. Univalent functions -- 4. Carathéodory?s prime ends theory -- 5. Hyperbolic geometry in simply connected domains -- 6. Quasi-geodesics and localization -- 7. Harmonic measures and Bloch functions -- Part II: Semigroups -- 8 Semigroups of holomorphic functions -- 9 Models and Koenigs functions -- 10 In?nitesimal generators -- 11 Extension to the boundary -- 12 Boundary ?xed points and in?nitesimal generators -- 13 Fixed points, backward invariant sets and petals -- 14 Contact points -- 15 Poles of the in?nitesimal generators -- 16 Rate of convergence at the Denjoy-Wolffpoint -- 17 Slopes of orbits at the Denjoy-Wolffpoint -- 18 Topological invariants. 330 $aThe book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aFunctions of complex variables 606 $aDynamics 606 $aErgodic theory 606 $aFunctional analysis 606 $aDifferential equations 606 $aGeometry 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 615 0$aFunctions of complex variables. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aFunctional analysis. 615 0$aDifferential equations. 615 0$aGeometry. 615 14$aFunctions of a Complex Variable. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aFunctional Analysis. 615 24$aOrdinary Differential Equations. 615 24$aGeometry. 676 $a512.2 700 $aBracci$b Filippo$4aut$4http://id.loc.gov/vocabulary/relators/aut$01005290 702 $aContreras$b Manuel D$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aDíaz-Madrigal$b Santiago$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418254503316 996 $aContinuous Semigroups of Holomorphic Self-maps of the Unit Disc$92311012 997 $aUNISA