Holomorphic Dynamics

This book, first published in 2000, is a graduate text on complex analytic dynamics - the mathematics behind things like the Mandelbrot set.

S. Morosawa (Author), Y. Nishimura (Author), M. Taniguchi (Author), T. Ueda (Author)

9780521662581, Cambridge University Press

Hardback, published 13 January 2000

352 pages, 12 b/w illus.
23.4 x 15.7 x 2.3 cm, 0.57 kg

This book, first published in 2000, 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, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an 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 Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.

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.

Subject Areas: Probability & statistics [PBT]