Complex Dynamics

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Springer Science & Business Media, 1993 - Mathematics - 174 pages
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Complex dynamics is today very much a focus of interest. Though several fine expository articles were available, by P. Blanchard and by M. Yu. Lyubich in particular, until recently there was no single source where students could find the material with proofs. For anyone in our position, gathering and organizing the material required a great deal of work going through preprints and papers and in some cases even finding a proof. We hope that the results of our efforts will be of help to others who plan to learn about complex dynamics and perhaps even lecture. Meanwhile books in the field a. re beginning to appear. The Stony Brook course notes of J. Milnor were particularly welcome and useful. Still we hope that our special emphasis on the analytic side will satisfy a need. This book is a revised and expanded version of notes based on lectures of the first author at UCLA over several \Vinter Quarters, particularly 1986 and 1990. We owe Chris Bishop a great deal of gratitude for supervising the production of course notes, adding new material, and making computer pictures. We have used his computer pictures, and we will also refer to the attractive color graphics in the popular treatment of H. -O. Peitgen and P. Richter. We have benefited from discussions with a number of colleagues, and from suggestions of students in both our courses.
  

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Contents

II
1
III
5
IV
9
V
11
VI
15
VII
17
VIII
19
IX
27
XXV
91
XXVI
93
XXVII
99
XXVIII
101
XXIX
103
XXX
105
XXXI
106
XXXII
109

X
31
XI
32
XII
33
XIII
35
XIV
41
XV
47
XVI
53
XVII
58
XVIII
63
XIX
65
XX
69
XXI
74
XXII
79
XXIII
81
XXIV
89
XXXIII
113
XXXIV
117
XXXV
123
XXXVI
133
XXXVII
136
XXXVIII
139
XXXIX
142
XL
148
XLI
153
XLII
161
XLIII
163
XLIV
171
XLV
175
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