Cargando…

Rotation sets and 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 Hubbar...

Descripción completa

Detalles Bibliográficos
Autor principal: Zakeri, Saeed
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-78810-4
http://cds.cern.ch/record/2629296
_version_ 1780959257766658048
author Zakeri, Saeed
author_facet Zakeri, Saeed
author_sort Zakeri, Saeed
collection CERN
description 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.
id cern-2629296
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2018
publisher Springer
record_format invenio
spelling cern-26292962021-04-21T18:46:22Zdoi:10.1007/978-3-319-78810-4http://cds.cern.ch/record/2629296engZakeri, SaeedRotation sets and complex dynamicsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:26292962018
spellingShingle Mathematical Physics and Mathematics
Zakeri, Saeed
Rotation sets and complex dynamics
title Rotation sets and complex dynamics
title_full Rotation sets and complex dynamics
title_fullStr Rotation sets and complex dynamics
title_full_unstemmed Rotation sets and complex dynamics
title_short Rotation sets and complex dynamics
title_sort rotation sets and complex dynamics
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-78810-4
http://cds.cern.ch/record/2629296
work_keys_str_mv AT zakerisaeed rotationsetsandcomplexdynamics