Holomorphic Dynamics: 66 (Cambridge Studies in Advanced Mathematics, Series Number 66) (English, S. Morosawa | Y. Nishimura | M. Taniguchi)

About the Book

This revised edition, published by Cambridge University Press, offers a thorough and mathematically unified exploration of holomorphic dynamics—the study of how analytic maps behave when iterated repeatedly over complex number spaces. Written for graduate students and research professionals, the text bridges classical complex analysis with modern developments, including the mathematics behind iconic structures like the Mandelbrot set and chaotic quadratic maps. The authors bring deep expertise to the subject, presenting a self-contained treatment that covers rational functions, entire functions, Kleinian groups, and polynomial automorphisms of several complex variables, such as complex Hénon maps. For Indian students and researchers seeking a rigorous yet accessible entry into complex dynamics and chaos theory, this book serves as an authoritative resource that connects foundational theory with cutting-edge applications in pure mathematics and the sciences.

Key Topics Covered

• Iteration of rational functions and the Mandelbrot set
• Entire functions and their dynamical properties
• Kleinian groups and complex analysis
• Polynomial automorphisms and complex Hénon maps
• Chaotic behaviour in quadratic maps and modern dynamics

Who Should Read This

Ideal for graduate students in pure mathematics, as well as professionals in science and technology fields—especially those in complex analysis, dynamical systems, and chaos theory. Indian researchers and advanced learners seeking a solid foundation in holomorphic dynamics, fractal geometry, or the mathematical underpinnings of nonlinear systems will find this book invaluable for both self-study and academic coursework.

352 pages · Revised Edition · Cambridge University Press · 13 January 2000