The Resource Complex Dynamics and Renormalization (AM-135), Curtis T. McMullen

Complex Dynamics and Renormalization (AM-135), Curtis T. McMullen

Label
Complex Dynamics and Renormalization (AM-135)
Title
Complex Dynamics and Renormalization (AM-135)
Statement of responsibility
Curtis T. McMullen
Creator
Contributor
Author
Provider
Subject
Language
  • eng
  • eng
Summary
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps
Cataloging source
DE-B1597
http://library.link/vocab/creatorName
McMullen, Curtis T
Government publication
other
LC call number
QC20.7.R43
LC item number
M36 1994eb
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
De Gruyter
Series statement
Annals of Mathematics Studies,
Series volume
135
http://library.link/vocab/subjectName
  • Dynamics
  • Mathematical physics
  • Polynomials
  • Renormalization (Physics)
Target audience
specialized
Label
Complex Dynamics and Renormalization (AM-135), Curtis T. McMullen
Instantiates
Publication
Copyright
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Chapter 7. Renormalization
  • Chapter 8. Puzzles and infinite renormalization
  • Chapter 9. Robustness
  • Chapter 10. Limits of renormalization
  • Chapter 11. Real quadratic polynomials
  • Appendix A. Orbifolds
  • Appendix B. A closing lemma for rational maps
  • Bibliography
  • Index
  • Frontmatter
  • Contents
  • Chapter 1. Introduction
  • Chapter 2. Background in conformal geometry
  • Chapter 3. Dynamics of rational maps
  • Chapter 4. Holomorphic motions and the Mandelbrot set
  • Chapter 5. Compactness in holomorphic dynamics
  • Chapter 6. Polynomials and external rays
Extent
1 online resource
Form of item
online
Isbn
9781400882557
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1515/9781400882557
Specific material designation
remote
System control number
  • (DE-B1597)467921
  • (OCoLC)954123972
  • (OCoLC)990384277
  • (DE-B1597)9781400882557
Label
Complex Dynamics and Renormalization (AM-135), Curtis T. McMullen
Publication
Copyright
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Chapter 7. Renormalization
  • Chapter 8. Puzzles and infinite renormalization
  • Chapter 9. Robustness
  • Chapter 10. Limits of renormalization
  • Chapter 11. Real quadratic polynomials
  • Appendix A. Orbifolds
  • Appendix B. A closing lemma for rational maps
  • Bibliography
  • Index
  • Frontmatter
  • Contents
  • Chapter 1. Introduction
  • Chapter 2. Background in conformal geometry
  • Chapter 3. Dynamics of rational maps
  • Chapter 4. Holomorphic motions and the Mandelbrot set
  • Chapter 5. Compactness in holomorphic dynamics
  • Chapter 6. Polynomials and external rays
Extent
1 online resource
Form of item
online
Isbn
9781400882557
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1515/9781400882557
Specific material designation
remote
System control number
  • (DE-B1597)467921
  • (OCoLC)954123972
  • (OCoLC)990384277
  • (DE-B1597)9781400882557

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...