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Rotation sets and complex dynamics

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Rotation sets and complex dynamics/ by Saeed Zakeri.
Author:	Zakeri, Saeed.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xiv, 124 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Set theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-78810-4
ISBN:	9783319788104

Rotation sets and complex dynamics
Zakeri, Saeed.

Rotation sets and complex dynamics[electronic resource] /by Saeed Zakeri. - Cham :Springer International Publishing :2018. - xiv, 124 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,22140075-8434 ;. - Lecture notes in mathematics ;1943..

1. Monotone Maps of the Circle -- 2. Rotation Sets -- 3. The Deployment Theorem -- 4. Applications and Computations -- 5. Relation to Complex Dynamics.

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.

ISBN: 9783319788104

Standard No.: 10.1007/978-3-319-78810-4doiSubjects--Topical Terms:

579942
Set theory.

LC Class. No.: QA248 / .Z354 2018

Dewey Class. No.: 511.322

Rotation sets and complex dynamics
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100 1 $a Zakeri, Saeed. $3 1206446
245 1 0 $a Rotation sets and complex dynamics $h [electronic resource] / $c by Saeed Zakeri.
260 $a Cham : $c 2018. $b Springer International Publishing : $b Imprint: Springer,
300 $a xiv, 124 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2214
505 0 $a 1. Monotone Maps of the Circle -- 2. Rotation Sets -- 3. The Deployment Theorem -- 4. Applications and Computations -- 5. Relation to Complex Dynamics.
520 $a 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.
650 0 $a Set theory. $3 579942
650 0 $a Rotational motion. $3 639866
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Functions of a Complex Variable. $3 672126
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773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 1943. $3 882220
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-78810-4
950 $a Mathematics and Statistics (Springer-11649)