An Introduction to Dynamical Systems

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Cambridge University Press, Jul 27, 1990 - Mathematics - 423 pages
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In recent years there has been an explosion of research centred on the appearance of so-called 'chaotic behaviour'. This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit this sort of behaviour. The early part of this 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, Anosov automorphism, the horseshoe diffeomorphism 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. This book, which has a great number of worked examples and exercises, many with hints, and over 200 figures, will be a valuable first textbook to both senior undergraduates and postgraduate students in mathematics, physics, engineering, and other areas in which the notions of qualitative dynamics are employed.
 

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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
69
XVII
72
XVIII
79
XIX
83
XX
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XXI
93
XXII
102
XXIII
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XXIV
108
XXV
119
XXVI
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XXVII
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XXVIII
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XXIX
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XXX
138
XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
180
XXXVII
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XXXIX
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XL
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L
248
LI
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LII
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LIII
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LV
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LVI
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LVII
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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
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LXXIII
345
LXXIV
355
LXXV
368
LXXVI
379
LXXVII
394
LXXVIII
413
LXXIX
417
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