Rotation Sets and Complex Dynamics
Seiten
2018
|
1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-78809-8 (ISBN)
Springer International Publishing (Verlag)
978-3-319-78809-8 (ISBN)
This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined.
The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields.
1. Monotone Maps of the Circle.- 2. Rotation Sets.- 3. The Deployment Theorem.- 4. Applications and Computations.- 5. Relation to Complex Dynamics.
| Erscheinungsdatum | 28.06.2018 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XIV, 124 p. 34 illus., 32 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 225 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | Circle Map • Complex Dynamics • Doubling Map • Dynamical Systems • External Ray • Julia set • Mandelbrot set • Rotation Cycle • Rotation number • Rotation Set |
| ISBN-10 | 3-319-78809-4 / 3319788094 |
| ISBN-13 | 978-3-319-78809-8 / 9783319788098 |
| Zustand | Neuware |
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