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Complex Dynamics: Twenty-Five Years after the Appearance of the Mandelbrot Set
 
Edited by: Robert L. Devaney Boston University, Boston, MA
Linda Keen Herbert H. Lehman College (CUNY), Bronx, NY
Complex Dynamics
eBook ISBN:  978-0-8218-7986-3
Product Code:  CONM/396.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Complex Dynamics
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Complex Dynamics: Twenty-Five Years after the Appearance of the Mandelbrot Set
Edited by: Robert L. Devaney Boston University, Boston, MA
Linda Keen Herbert H. Lehman College (CUNY), Bronx, NY
eBook ISBN:  978-0-8218-7986-3
Product Code:  CONM/396.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3962006; 206 pp
    MSC: Primary 37; Secondary 30; 54;

    Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Fatou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.

    Readership

    Graduate students and research mathematicians interested in complex analysis and dynamical systems.

  • Table of Contents
     
     
    • Articles
    • Douglas K. Childers, John C. Mayer, H. Murat Tuncali and E. D. Tymchatyn — Indecomposable continua and the Julia sets of rational maps [ MR 2209083 ]
    • Eric Bedford and John Smillie — The Hénon family: the complex horseshoe locus and real parameter space [ MR 2209084 ]
    • Robert L. Devaney — Baby Mandelbrot sets adorned with halos in families of rational maps [ MR 2209085 ]
    • Robert L. Devaney, Matt Holzer and David Uminsky — Blowup points and baby Mandelbrot sets for singularly perturbed rational maps [ MR 2209086 ]
    • Romain Dujardin — Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms [ MR 2209087 ]
    • Suzanne Lynch Hruska — Rigorous numerical studies of the dynamics of polynomial skew products of ${\Bbb C}^2$ [ MR 2209088 ]
    • Linda Keen and Nikola Lakic — Accumulation points of iterated function systems [ MR 2209089 ]
    • Linda Keen and Shenglan Yuan — Parabolic perturbation of the family $\lambda \tan z$ [ MR 2209090 ]
    • Kevin M. Pilgrim — Polynomial vector fields, dessins d’enfants, and circle packings [ MR 2209091 ]
    • James T. Rogers, Jr. — Siegel disks whose boundaries have only two complementary domains [ MR 2209092 ]
    • Kimberly A. Roth — Non-uniform porosity for a subset of some Julia sets [ MR 2210774 ]
    • Bartłomiej Skorulski — The existence of conformal measures for some transcendental meromorphic functions [ MR 2210775 ]
    • Robert L. Devaney and Linda Keen — Open problems [ MR 2210776 ]
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3962006; 206 pp
MSC: Primary 37; Secondary 30; 54;

Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Fatou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.

Readership

Graduate students and research mathematicians interested in complex analysis and dynamical systems.

  • Articles
  • Douglas K. Childers, John C. Mayer, H. Murat Tuncali and E. D. Tymchatyn — Indecomposable continua and the Julia sets of rational maps [ MR 2209083 ]
  • Eric Bedford and John Smillie — The Hénon family: the complex horseshoe locus and real parameter space [ MR 2209084 ]
  • Robert L. Devaney — Baby Mandelbrot sets adorned with halos in families of rational maps [ MR 2209085 ]
  • Robert L. Devaney, Matt Holzer and David Uminsky — Blowup points and baby Mandelbrot sets for singularly perturbed rational maps [ MR 2209086 ]
  • Romain Dujardin — Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms [ MR 2209087 ]
  • Suzanne Lynch Hruska — Rigorous numerical studies of the dynamics of polynomial skew products of ${\Bbb C}^2$ [ MR 2209088 ]
  • Linda Keen and Nikola Lakic — Accumulation points of iterated function systems [ MR 2209089 ]
  • Linda Keen and Shenglan Yuan — Parabolic perturbation of the family $\lambda \tan z$ [ MR 2209090 ]
  • Kevin M. Pilgrim — Polynomial vector fields, dessins d’enfants, and circle packings [ MR 2209091 ]
  • James T. Rogers, Jr. — Siegel disks whose boundaries have only two complementary domains [ MR 2209092 ]
  • Kimberly A. Roth — Non-uniform porosity for a subset of some Julia sets [ MR 2210774 ]
  • Bartłomiej Skorulski — The existence of conformal measures for some transcendental meromorphic functions [ MR 2210775 ]
  • Robert L. Devaney and Linda Keen — Open problems [ MR 2210776 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.