Dimension Theory in Dynamical Systems: Contemporary Views and Applications

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University of Chicago Press, 1997 - Mathematics - 304 pages
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The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior.

In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field.

Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
  

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Contents

IV
11
V
12
VI
16
VII
21
VIII
28
IX
31
X
34
XI
35
XXV
133
XXVI
140
XXVII
153
XXVIII
170
XXIX
174
XXX
182
XXXI
189
XXXII
196

XII
41
XIII
48
XIV
57
XV
61
XVI
64
XVII
65
XVIII
68
XIX
83
XX
87
XXI
110
XXII
115
XXIII
117
XXIV
123
XXXIII
197
XXXIV
209
XXXV
227
XXXVI
247
XXXVII
259
XXXVIII
270
XXXIX
271
XL
279
XLI
293
XLII
295
XLIII
301
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About the author (1997)

Yakov B. Pesin is professor of mathematics at Pennsylvania State University, University Park. He is the author of The General Theory of Smooth Hyperbolic Dynamical Systems and co-editor of Sinai's Moscow Seminar on Dynamical Systems.

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