| Dewey Class |
515.9 |
| Title |
Continuous Semigroups of Holomorphic Self-maps of the Unit Disc ([EBook]) / by Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal. |
| Author |
Bracci, Filippo |
| Added Personal Name |
Contreras, Manuel D. |
| Díaz-Madrigal, Santiago |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2020. |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2020. |
| Physical Details |
XXVII, 566 p. 18 illus. : online resource. |
| Series |
Springer monographs in mathematics 1439-7382 |
| ISBN |
9783030367824 |
| Summary Note |
The 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.: |
| Contents note |
Part 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. |
| Mode of acces to digital resource |
Digital 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 |
| System details note |
- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-36782-4 |
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