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
IV
7
V
12
VI
16
VII
20
VIII
27
IX
29
XXXVI
112
XXXVIII
119
XXXIX
124
XL
127
XLI
132
XLII
141
XLIII
149
XLIV
163

X
32
XI
35
XII
41
XIII
42
XIV
45
XV
47
XVI
49
XVII
54
XIX
57
XX
62
XXI
64
XXII
69
XXIII
73
XXV
77
XXVI
80
XXVII
85
XXVIII
86
XXIX
88
XXX
93
XXXI
96
XXXII
97
XXXIII
100
XXXIV
105
XXXV
106
XLV
173
XLVI
179
XLVII
187
XLVIII
198
XLIX
209
L
214
LI
220
LII
225
LIII
235
LIV
241
LV
251
LVI
263
LVII
264
LVIII
270
LIX
276
LX
288
LXI
295
LXII
304
LXIII
310
LXIV
318
LXV
321
LXVI
329
LXVII
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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