Holomorphic Dynamics by S. MorosawaHolomorphic Dynamics by S. Morosawa

Holomorphic Dynamics

byS. Morosawa, Y. Nishimura, M. Taniguchi

Hardcover | January 13, 2000

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Here is a comprehensive introduction to holomorphic dynamics, that is, the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, for example, with the discovery of the Mandelbrot set, and work on chaotic behavior of quadratic maps. The mathematically unified treatment emphasizes the substantial role of classical complex analysis in understanding holomorphic dynamics and offers up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Hénon maps, as well as the case of rational functions.
Title:Holomorphic DynamicsFormat:HardcoverDimensions:352 pages, 8.98 × 5.98 × 0.94 inPublished:January 13, 2000Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521662583

ISBN - 13:9780521662581


Table of Contents

1. The dynamics of polynomial maps; 2. Fatou and Julia sets; 3. Dynamics of entire functions; 4. Dynamics of rational functions; 5. Kleinian groups and Sullivan's dictionary; 6. The dynamics of holomorphic maps of sveral variables; 7. Dynamics of generalized Hénon maps; 8. Pluripotential theory of polynomial automorphisms; 9. Dynamics of polynomial automorphisms; Bibliography; Index.

From Our Editors

Everyone knows numbers are the focal point of mathematics. However, not many people know the importance of complex number spaces, as explained in Holomorphic Dynamics. In this text, readers will learn about the iteration of analytic maps in complex number spaces, including the discovery of the Mandelbrot set. The volume also focusses on the role of classical complex analysis in holomorphic dynamics and other variables such as complex Henon maps and rational functions. It contains 12 line diagrams and will be of interest to professionals and students of mathematics.