An Introduction to Dynamical Systems

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Cambridge University Press, Jul 27, 1990 - Mathematics - 423 pages
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Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior." The first portion of the book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms and the logistic map and area-preserving planar maps. The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. The text contains many worked examples and exercises, many with hints. It will be a valuable first textbook for senior undergraduate and postgraduate students of mathematics, physics, and engineering.
 

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Contents

II
1
III
5
IV
6
V
11
VI
16
VII
20
VIII
28
IX
33
XLI
206
XLIII
211
XLIV
215
XLV
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XLVI
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XLVII
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XLVIII
234
XLIX
245

X
38
XI
42
XII
56
XIII
64
XV
67
XVI
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XVII
72
XVIII
79
XIX
83
XX
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XXI
93
XXII
102
XXIII
105
XXIV
108
XXV
119
XXVI
120
XXVII
123
XXVIII
125
XXIX
132
XXX
138
XXXI
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XXXII
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XXXIII
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XXXIV
154
XXXV
170
XXXVI
180
XXXVII
190
XXXIX
199
XL
203
L
248
LI
253
LII
258
LIII
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LV
264
LVI
268
LVII
271
LVIII
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LIX
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LX
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LXI
282
LXII
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LXIII
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LXIV
302
LXVI
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LXVII
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LXVIII
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LXIX
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LXXI
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LXXII
338
LXXIII
345
LXXIV
355
LXXV
368
LXXVI
379
LXXVII
394
LXXVIII
413
LXXIX
417
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