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Könyv Rotation Sets and Complex Dynamics Saeed Zakeri

Rotation Sets and Complex Dynamics

Szerző: Saeed Zakeri
Nyelv: Angol
Kötés: Puha kötésű
Kiadó: Springer International Publishing AG
Elérhetőség: Beszállítói készleten alacsony példányszámban
Küldés 13-18 napon belül
20 693 Ft
This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation t...

Információk a könyvről

Szerző
Saeed Zakeri
Nyelv
Angol
Kötés
Könyv - Puha kötésű
Kiadva
2018
oldal
124
EAN
9783319788098
ISBN
3319788094
Enbook ID
19042388
Kiadó
Springer International Publishing AG
Súly
454
Méretek
159 x 235 x 28

Teljes leírás

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.

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