Introduction to the Modern Theory of Dynamical Systems

Front Cover
Cambridge University Press, 1997 - Mathematics - 802 pages
2 Reviews
This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises.
  

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Contents

I
vii
II
xiii
III
1
IV
6
V
8
VI
10
VII
13
VIII
15
LXXIX
405
LXXX
410
LXXXI
412
LXXXII
415
LXXXIII
419
LXXXIV
423
LXXXV
424
LXXXVI
425

IX
19
X
26
XI
28
XII
32
XIII
35
XIV
39
XV
42
XVI
47
XVII
57
XIX
64
XX
68
XXI
71
XXII
79
XXIII
87
XXIV
90
XXV
94
XXVI
100
XXVII
105
XXIX
119
XXX
128
XXXI
133
XXXIII
146
XXXIV
161
XXXV
173
XXXVI
179
XXXVII
183
XXXVIII
196
XXXIX
200
XL
205
XLI
219
XLII
229
XLIII
233
XLIV
235
XLV
237
XLVII
239
XLVIII
260
XLIX
263
L
273
LI
278
LII
287
LIV
290
LV
298
LVI
304
LVII
307
LVIII
308
LIX
310
LX
316
LXI
318
LXII
323
LXIII
326
LXIV
330
LXV
335
LXVI
336
LXVII
339
LXVIII
349
LXIX
365
LXX
367
LXXI
372
LXXII
376
LXXIII
379
LXXIV
381
LXXV
387
LXXVI
393
LXXVII
401
LXXVIII
403
LXXXVII
434
LXXXVIII
441
LXXXIX
447
XC
451
XCI
452
XCII
457
XCIII
460
XCIV
464
XCV
470
XCVI
479
XCVII
483
XCVIII
489
XCIX
493
C
500
CI
505
CII
511
CIII
514
CIV
519
CV
520
CVI
525
CVII
526
CVIII
529
CIX
531
CX
532
CXI
537
CXII
541
CXIII
549
CXIV
551
CXV
555
CXVI
559
CXVII
565
CXVIII
571
CXIX
574
CXX
581
CXXI
583
CXXII
587
CXXIII
591
CXXIV
597
CXXV
608
CXXVI
615
CXXVII
623
CXXVIII
628
CXXIX
637
CXXX
643
CXXXI
651
CXXXII
657
CXXXIII
659
CXXXIV
660
CXXXV
672
CXXXVI
678
CXXXVII
693
CXXXVIII
701
CXXXIX
703
CXL
711
CXLI
715
CXLII
727
CXLIII
730
CXLIV
731
CXLV
735
CXLVI
738
CXLVII
741
CXLVIII
765
CXLIX
781
CL
793
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About the author (1997)

Anatole Katok is Raymond N. Shibley Professor of Mathematics at Pennsylvania State University.

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