Dimension Theory in Dynamical Systems: Contemporary Views and Applications (Chicago Lectures in Mathematics)

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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Provides a systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes important accomplishments in the field. Topics include the general concept of dimension, the dimension interpretation of well- known invariants of dynamical systems, formulas of dimension of some well-known hyperbolic invariant sets, mathematical analysis of dimension used in applied research, and mathematical theory of invariant multifractals. For advanced mathematicians, scientists who depend on mathematical modeling of dynamical processes, and advanced students in the theory of dynamical systems and dimension theory. Annotation c. by Book News, Inc., Portland, Or.