Celebrate the holidays with Apress Access for just $/£/€ 99!

Lecture Notes in Mathematics

Rotation Sets and Complex Dynamics

Authors: Zakeri, Saeed

Free Preview
  • Provides the first systematic treatment of rotation sets
     
    The abstract treatment is augmented by concrete examples of applications in polynomial dynamics
     
    The clear and detailed exposition is accompanied by numerous illustrations, making it accessible to graduate students

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-78810-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-78809-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-78810-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-78809-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

Services for this book

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Rotation Sets and Complex Dynamics
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2214
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-78810-4
DOI
10.1007/978-3-319-78810-4
Softcover ISBN
978-3-319-78809-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 124
Number of Illustrations
2 b/w illustrations, 32 illustrations in colour
Topics