An introduction to julia and fatou sets

Scott Sutherland

doi:10.1007/978-3-319-08105-2__3

An introduction to julia and fatou sets

Scott Sutherland

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We give an elementary introduction to the holomorphic dynamics of mappings on the Riemann sphere, with a focus on Julia and Fatou sets. Our main emphasis is on the dynamics of polynomials, especially quadratic polynomials.

Original language	English
Title of host publication	Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets
Editors	V. Kannan, Michael F. Barnsley, Robert L. Devaney, Vinod Kumar P.B., Kenneth J. Devaney, Christoph Bandt
Publisher	Springer New York LLC
Pages	37-60
Number of pages	24
ISBN (Electronic)	9783319081045
DOIs	https://doi.org/10.1007/978-3-319-08105-2__3
State	Published - 2014
Event	1st International Conference and Workshop on Fractals and Wavelets, ICFW India - Kochi, India Duration: Nov 13 2013 → Nov 16 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	92
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	1st International Conference and Workshop on Fractals and Wavelets, ICFW India
Country/Territory	India
City	Kochi
Period	11/13/13 → 11/16/13

Keywords

Böttcher coordinate
Cremer point
Fatou set
Holomorphic dynamical systems
Julia set
Normal family
Parabolic orbit
Siegel disk

Access to Document

10.1007/978-3-319-08105-2__3

Cite this

Sutherland, S. (2014). An introduction to julia and fatou sets. In V. Kannan, M. F. Barnsley, R. L. Devaney, V. K. P.B., K. J. Devaney, & C. Bandt (Eds.), Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets (pp. 37-60). (Springer Proceedings in Mathematics and Statistics; Vol. 92). Springer New York LLC. https://doi.org/10.1007/978-3-319-08105-2__3

Sutherland, Scott. / An introduction to julia and fatou sets. Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets. editor / V. Kannan ; Michael F. Barnsley ; Robert L. Devaney ; Vinod Kumar P.B. ; Kenneth J. Devaney ; Christoph Bandt. Springer New York LLC, 2014. pp. 37-60 (Springer Proceedings in Mathematics and Statistics).

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title = "An introduction to julia and fatou sets",

abstract = "We give an elementary introduction to the holomorphic dynamics of mappings on the Riemann sphere, with a focus on Julia and Fatou sets. Our main emphasis is on the dynamics of polynomials, especially quadratic polynomials.",

keywords = "B{\"o}ttcher coordinate, Cremer point, Fatou set, Holomorphic dynamical systems, Julia set, Normal family, Parabolic orbit, Siegel disk",

author = "Scott Sutherland",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.; 1st International Conference and Workshop on Fractals and Wavelets, ICFW India ; Conference date: 13-11-2013 Through 16-11-2013",

year = "2014",

doi = "10.1007/978-3-319-08105-2\_\_3",

language = "English",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "37--60",

editor = "V. Kannan and Barnsley, \{Michael F.\} and Devaney, \{Robert L.\} and P.B., \{Vinod Kumar\} and Devaney, \{Kenneth J.\} and Christoph Bandt",

booktitle = "Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets",

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Sutherland, S 2014, An introduction to julia and fatou sets. in V Kannan, MF Barnsley, RL Devaney, VK P.B., KJ Devaney & C Bandt (eds), Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets. Springer Proceedings in Mathematics and Statistics, vol. 92, Springer New York LLC, pp. 37-60, 1st International Conference and Workshop on Fractals and Wavelets, ICFW India, Kochi, India, 11/13/13. https://doi.org/10.1007/978-3-319-08105-2__3

An introduction to julia and fatou sets. / Sutherland, Scott.
Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets. ed. / V. Kannan; Michael F. Barnsley; Robert L. Devaney; Vinod Kumar P.B.; Kenneth J. Devaney; Christoph Bandt. Springer New York LLC, 2014. p. 37-60 (Springer Proceedings in Mathematics and Statistics; Vol. 92).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We give an elementary introduction to the holomorphic dynamics of mappings on the Riemann sphere, with a focus on Julia and Fatou sets. Our main emphasis is on the dynamics of polynomials, especially quadratic polynomials.

AB - We give an elementary introduction to the holomorphic dynamics of mappings on the Riemann sphere, with a focus on Julia and Fatou sets. Our main emphasis is on the dynamics of polynomials, especially quadratic polynomials.

KW - Böttcher coordinate

KW - Cremer point

KW - Fatou set

KW - Holomorphic dynamical systems

KW - Julia set

KW - Normal family

KW - Parabolic orbit

KW - Siegel disk

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A2 - P.B., Vinod Kumar

A2 - Devaney, Kenneth J.

A2 - Bandt, Christoph

PB - Springer New York LLC

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Sutherland S. An introduction to julia and fatou sets. In Kannan V, Barnsley MF, Devaney RL, P.B. VK, Devaney KJ, Bandt C, editors, Fractals, Wavelets and their Applications - Contributions from the International Conference and Workshop on Fractals and Wavelets. Springer New York LLC. 2014. p. 37-60. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-319-08105-2__3

An introduction to julia and fatou sets

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