國立虎尾科技大學 |

Rotation Sets and Complex Dynamics

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Rotation Sets and Complex Dynamics/ by Saeed Zakeri.
作者:	Zakeri, Saeed.
面頁冊數:	XIV, 124 p. 34 illus., 32 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Dynamics. -
電子資源:	https://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. - 1st ed. 2018. - XIV, 124 p. 34 illus., 32 illus. in color.online resource. - Lecture Notes in Mathematics,22140075-8434 ;. - Lecture Notes in Mathematics,2144.

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:

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Rotation Sets and Complex Dynamics
LDR:02754nam a22004215i 4500 001 994986
003 DE-He213
005 20200704104945.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319788104 $9 978-3-319-78810-4
024 7 $a 10.1007/978-3-319-78810-4 $2 doi
035 $a 978-3-319-78810-4
050 4 $a QA313
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBWR $2 thema
082 0 4 $a 515.39 $2 23
082 0 4 $a 515.48 $2 23
100 1 $a Zakeri, Saeed. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1206446
245 1 0 $a Rotation Sets and Complex Dynamics $h [electronic resource] / $c by Saeed Zakeri.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XIV, 124 p. 34 illus., 32 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Functions of complex variables. $3 528649
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Functions of a Complex Variable. $3 672126
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319788098
776 0 8 $i Printed edition: $z 9783319788111
830 0 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2144 $3 1254300
856 4 0 $u https://doi.org/10.1007/978-3-319-78810-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-LNM
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)