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Synopsis
A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.
"synopsis" may belong to another edition of this title.
Synopsis
Complex Dynamics discusses the properties of conformal mappings in the complex plane, a subject that is closely connected to the study of fractals and chaos. Indeed the culmination of the book is a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. The book focuses on the analytic side of this contemporary subject. The text was developed out of a course taught over several semesters; its focus is to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration (the Julia set), classification of periodic components, critical points and expanding maps, some applications of conformal mappings (e.g. Hermann rings), the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.
"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date1993
- ISBN 10 0387979425
- ISBN 13 9780387979427
- BindingPaperback
- Number of pages201
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Complex Dynamics
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Spinger-Verlag, 1993
ISBN 10: 0387979425
ISBN 13: 9780387979427
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Complex Dynamics (Universitext)
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Complex Dynamics (Universitext)
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Complex Dynamics (Universitext) by Carleson, Lennart [Paperback ]
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