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MARC 21

Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
Tag	Description
020	$a9783030367824
082	$a515.9
099	$aOnline resource: Springer
100	$aBracci, Filippo.$eauthor.
245	$aContinuous Semigroups of Holomorphic Self-maps of the Unit Disc$h[EBook]$cby Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal.
250	$a1st ed. 2020.
260	$aCham :$bSpringer International Publishing :$bImprint: Springer,$c2020.
300	$aXXVII, 566 p. 18 illus.$bonline resource.
336	$atext
338	$aonline resource
440	$aSpringer Monographs in Mathematics,$x1439-7382
505	$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 Inﬁnitesimal generators -- 11 Extension to the boundary -- 12 Boundary ﬁxed points and inﬁnitesimal generators -- 13 Fixed points, backward invariant sets and petals -- 14 Contact points -- 15 Poles of the inﬁnitesimal generators -- 16 Rate of convergence at the Denjoy-Wolffpoint -- 17 Slopes of orbits at the Denjoy-Wolffpoint -- 18 Topological invariants.
520	$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.
533	$aDigital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
538	$a - Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aContreras, Manuel D.$eauthor.
700	$aDíaz-Madrigal, Santiago.$eauthor.
710	$aSpringerLink (Online service)
830	$aSpringer Monographs in Mathematics,$x1439-7382
856	$uhttps://doi.org/10.1007/978-3-030-36782-4