Rotation Sets And Complex Dynamics

June 24, 2018|
Rotation Sets And Complex Dynamics by Saeed Zakeri
Earn 363 plum® points
Buy Online
Ship to an address
Free shipping on orders over $35
Pick up in store
To see if pickup is available,
Buy In Store
Not sold in stores
Prices and offers may vary in store


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.
Title:Rotation Sets And Complex Dynamics
Product dimensions:124 pages, 9.41 X 7.24 X 0.98 in
Shipping dimensions:124 pages, 9.41 X 7.24 X 0.98 in
Published:June 24, 2018
Publisher:Springer Nature
Appropriate for ages:All ages
ISBN - 13:9783319788098

Look for similar items by category:

Recently Viewed