Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics

Front Cover
Springer Science & Business Media, Apr 1, 1998 - Mathematics - 474 pages
1 Review
The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

III
1
IV
5
V
9
VI
13
VII
17
VIII
19
IX
31
X
37
LV
251
LVI
252
LVII
258
LVIII
261
LIX
264
LX
268
LXI
270
LXII
273

XII
41
XIII
47
XIV
51
XV
58
XVI
65
XVII
71
XVIII
79
XIX
83
XX
85
XXI
86
XXII
88
XXIII
95
XXIV
100
XXV
102
XXVI
105
XXVII
112
XXVIII
123
XXIX
125
XXX
129
XXXI
136
XXXII
139
XXXIV
144
XXXV
153
XXXVI
156
XXXVII
165
XXXVIII
172
XXXIX
175
XL
183
XLI
189
XLII
190
XLIII
191
XLIV
195
XLV
199
XLVI
205
XLVII
210
XLVIII
215
XLIX
226
L
232
LI
241
LII
244
LIII
246
LIV
247
LXIII
277
LXIV
280
LXV
283
LXVI
289
LXVII
292
LXVIII
295
LXIX
300
LXX
303
LXXI
304
LXXII
306
LXXIII
311
LXXIV
315
LXXV
320
LXXVI
327
LXXVII
330
LXXVIII
333
LXXIX
335
LXXX
344
LXXXI
346
LXXXII
351
LXXXIII
355
LXXXIV
359
LXXXV
364
LXXXVI
368
LXXXVII
371
LXXXVIII
378
LXXXIX
386
XC
388
XCI
391
XCII
393
XCIII
397
XCIV
405
XCV
411
XCVI
417
XCVII
420
XCVIII
425
XCIX
432
C
449
CI
457
CII
461
Copyright

Other editions - View all

Common terms and phrases

Popular passages

Page 451 - Lasota A, and Mackey MC (1989) Stochastic perturbation of dynamical systems: the weak convergence of measures, J.

References to this book

All Book Search results »

Bibliographic information