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Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

ΣΥΓΓΡΑΦΕΙΣ
Bracci Filippo Contreras Manuel D. Diaz-Madrigal Santiago
Τιμή
99,10 €
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Δωρεάν μεταφορικά

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.
Συγγραφείς: Bracci Filippo, Contreras Manuel D., Diaz-Madrigal Santiago
Εκδότης: SPRINGER
Σελίδες: 556
ISBN: 9783030367848
Εξώφυλλο: Μαλακό Εξώφυλλο
Αριθμός Έκδοσης: 1
Έτος έκδοσης: 2020

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

Dipartimento di Matematica, Università di Roma “Tor Vergata”, Roma, Italy

Departamento de Matemática Aplicada II and IMUS, Universidad de Sevilla, Sevilla, Spain

Departamento de Matemática Aplicada II and IMUS, Universidad de Sevilla, Sevilla, Spain

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