Holomorphic Dynamics

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Cambridge University Press, Jan 13, 2000 - Mathematics - 338 pages
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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.
 

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Contents

II
1
III
2
V
7
VI
12
VII
16
VIII
20
IX
27
X
29
XXXIX
112
XLI
119
XLII
124
XLIII
127
XLIV
132
XLV
141
XLVI
149
XLVII
163

XI
32
XII
35
XIII
41
XV
42
XVII
45
XVIII
47
XIX
49
XX
54
XXII
57
XXIII
62
XXIV
64
XXV
69
XXVI
73
XXVIII
77
XXIX
80
XXX
85
XXXI
86
XXXII
88
XXXIII
93
XXXIV
96
XXXV
97
XXXVI
100
XXXVII
105
XXXVIII
106
XLVIII
173
XLIX
179
L
187
LI
198
LII
209
LIII
214
LIV
220
LV
225
LVI
235
LVII
241
LVIII
251
LIX
263
LX
264
LXI
270
LXII
276
LXIII
288
LXIV
295
LXV
304
LXVI
310
LXVII
318
LXVIII
321
LXIX
329
LXX
335
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Page 329 - The exponent of convergence of Poincare series. Proc. London Math. Soc. (3) 18 (1968), 461-483; MR 37 # 2986.
Page 333 - Smale, S. On the existence of generally convergent algorithms. J. Complexity, 2: 2-11, 1986.

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