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Cambridge University Press
Holomorphic Dynamics

Holomorphic Dynamics


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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.

Product Details

ISBN-13: 9780521662581
Publisher: Cambridge University Press
Publication date: 01/28/2013
Series: Cambridge Studies in Advanced Mathematics Series , #66
Edition description: Revised Edition
Pages: 350
Product dimensions: 5.98(w) x 8.98(h) x 0.91(d)

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.

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