No Holomorphic Continuous on Boundary of Unit Disk and 1z
The Resource Continuous Semigroups of Holomorphic Self-maps of the Unit Disc, by Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal, (electronic resource)
Continuous Semigroups of Holomorphic Self-maps of the Unit Disc, by Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal, (electronic resource)
- Title
- Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
- Statement of responsibility
- by Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
- Creator
-
- Bracci, Filippo
- Contributor
-
- Díaz-Madrigal, Santiago
- Contreras, Manuel D
- SpringerLink (Online service)
- Subject
-
- Dynamics
- Ergodic theory
- Functional analysis
- Geometry
- Differential equations
- Functions of complex variables
- Language
- eng
- Summary
- 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
- Member of
-
- Springer Monographs in Mathematics,
- Is part of
-
- Springer eBooks
- http://library.link/vocab/creatorName
- Bracci, Filippo
- Literary form
- non fiction
- Nature of contents
- dictionaries
- http://library.link/vocab/relatedWorkOrContributorName
-
- Contreras, Manuel D
- Díaz-Madrigal, Santiago
- SpringerLink (Online service)
- Series statement
- Springer Monographs in Mathematics,
- http://library.link/vocab/subjectName
-
- Functions of complex variables
- Dynamics
- Ergodic theory
- Functional analysis
- Differential equations
- Geometry
- Instantiates
-
- Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
- Publication
-
- Cham, Springer International Publishing | Imprint: Springer, 2020
- Contents
- 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 In{uFB01}nitesimal generators -- 11 Extension to the boundary -- 12 Boundary {uFB01}xed points and in{uFB01}nitesimal generators -- 13 Fixed points, backward invariant sets and petals -- 14 Contact points -- 15 Poles of the in{uFB01}nitesimal generators -- 16 Rate of convergence at the Denjoy-Wolffpoint -- 17 Slopes of orbits at the Denjoy-Wolffpoint -- 18 Topological invariants
- Control code
- ssj0002287032
- Dimensions
- unknown
- Edition
- 1st ed. 2020
- Extent
- 1 online resource (XXVII, 566 p. 18 illus.)
- Form of item
- online
- Governing access note
- Access restricted to subscribing institutions
- Isbn
- 9783030367817
- Isbn Type
- (print)
- Other control number
- 10.1007/978-3-030-36782-4
- Other physical details
- online resource
- Specific material designation
- remote
- System control number
- (WaSeSS)ssj0002287032
- Publication
-
- Cham, Springer International Publishing | Imprint: Springer, 2020
- Contents
- 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 In{uFB01}nitesimal generators -- 11 Extension to the boundary -- 12 Boundary {uFB01}xed points and in{uFB01}nitesimal generators -- 13 Fixed points, backward invariant sets and petals -- 14 Contact points -- 15 Poles of the in{uFB01}nitesimal generators -- 16 Rate of convergence at the Denjoy-Wolffpoint -- 17 Slopes of orbits at the Denjoy-Wolffpoint -- 18 Topological invariants
- Control code
- ssj0002287032
- Dimensions
- unknown
- Edition
- 1st ed. 2020
- Extent
- 1 online resource (XXVII, 566 p. 18 illus.)
- Form of item
- online
- Governing access note
- Access restricted to subscribing institutions
- Isbn
- 9783030367817
- Isbn Type
- (print)
- Other control number
- 10.1007/978-3-030-36782-4
- Other physical details
- online resource
- Specific material designation
- remote
- System control number
- (WaSeSS)ssj0002287032
Source: http://link.bowdoin.edu/portal/Continuous-Semigroups-of-Holomorphic-Self-maps-of/UDzqYSONdfo/
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