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Complex dynamical systems : the mathematics behind the Mandelbrot and Julia sets / Robert L. Devaney, editor ; Bodil Branner [and six others].
- Format:
- Book
- Author/Creator:
- Branner, Bodil, author.
- Series:
- Proceedings of symposia in applied mathematics. AMS short course lecture notes ; Volume 49.
- Proceedings of Symposia in Applied Mathematics : AMS Short Course Lecture Notes ; Volume 49
- Language:
- English
- Subjects (All):
- Differentiable dynamical systems--Congresses.
- Differentiable dynamical systems.
- Physical Description:
- 1 online resource (223 p.)
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 1994.
- Language Note:
- English
- Summary:
- The Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.
- Contents:
- ""Contents""; ""Preface""; ""The Complex Dynamics of Quadratic Polynomials""; ""Puzzles and Para-Puzzles of Quadratic and Cubic Polynomials""; ""Julia Sets of Rational Maps""; ""Does a Julia Set Depend Continuously on the Polynomial?""; ""The Dynamics of Newton's Method""; ""The Spider Algorithm""; ""Complex Dynamics and Entire Functions""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Y""
- Notes:
- Lecture notes prepared for the American Mathematical Society Short Course, Complex Dynamical Systems, held in Cincinnati, Ohio January 10-11, 1994"--T.p. verso.
- Includes bibliographical references at the end of each chapters and index.
- Description based on print version record.
- ISBN:
- 0-8218-9264-9
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