Integrability and Nonintegrability in Geometry and Mechanics

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Springer Science & Business Media, Nov 30, 1988 - Mathematics - 343 pages
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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . 1111 Oulik'. n. . Chi" . ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
  

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Contents

II
1
III
6
IV
10
V
12
VI
17
VII
20
VIII
30
IX
32
XXXIX
171
XL
173
XLII
176
XLIII
178
XLIV
181
XLV
182
XLVI
184
XLVII
186

X
34
XI
39
XII
44
XIII
46
XIV
55
XV
68
XVI
70
XVII
73
XVIII
78
XIX
91
XXI
92
XXII
97
XXIII
98
XXIV
99
XXV
103
XXVI
109
XXVII
111
XXVIII
116
XXIX
123
XXX
126
XXXI
129
XXXII
143
XXXIII
146
XXXIV
149
XXXV
157
XXXVI
160
XXXVII
165
XXXVIII
167
XLVIII
187
XLIX
189
L
207
LI
210
LII
216
LIII
220
LIV
231
LV
236
LVI
243
LVII
250
LVIII
256
LIX
260
LX
261
LXI
266
LXII
267
LXIII
272
LXIV
275
LXV
277
LXVI
281
LXVII
287
LXVIII
291
LXIX
294
LXX
300
LXXI
311
LXXII
324
LXXIII
326
LXXIV
341
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Symplectic Geometry
A.T. Fomenko
Limited preview - 1995
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