Rotation Sets and Complex Dynamics (Lecture Notes in Mathematics, Band 2214) - Softcover

Buch 19 von 20: Lecture Notes in Mathematics

Zakeri, Saeed

 
9783319788098: Rotation Sets and Complex Dynamics (Lecture Notes in Mathematics, Band 2214)
Softcover
ISBN 10: 3319788094 ISBN 13: 9783319788098
Verlag: Springer, 2018

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

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.



„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2018
Sprache
Englisch
ISBN 10 
3319788094
ISBN 13 
9783319788098
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
140
Kontakt zum Hersteller
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

Europaplatz 3,69115 Heidelberg, Germany
Heidelberg
69115
Deutschland

Weitere beliebte Ausgaben desselben Titels

9783319788111: Rotation Sets and Complex Dynamics

Vorgestellte Ausgabe

ISBN 10:  3319788116 ISBN 13:  9783319788111
Verlag: Springer, 2018
Softcover