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Dimension Theory in Dynamical Systems : Contemporary Views and Applications.

Author: Yakov B Pesin
Publisher: Chicago : University of Chicago Press, 1997.
Series: Chicago lectures in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Yakov B Pesin
ISBN: 9780226662237 0226662233
OCLC Number: 437247587
Description: 1 online resource (320 pages).
Contents: Dimention Theory in Dynamical Systems; Contents; Preface; Introduction; Part I: Carathéodory Dimension Characteristics; Chapter 1. General Carathéodory Construction; Chapter 2. C-Structures Associated with Metrics: Hausdorff Dimension and Box Dimension; Chapter 3. C-Structures Associated with Metrics and Measures: Dimension Spectra; Appendix I: Hausdorff (Box) Dimension and Q-(Box) Dimension of Sets and Measures in General Metric Spaces; Chapter 4. C-Structures Associated with Dynamical Systems: Thermodynamic Formalism; Appendix II: Variational Principle for Topological Pressure. Symbolic Dynamical Systems Bowen's Equation; Appendix III: An Example of Carathéodory Structure Generated by Dynamical Systems; Part II: Applications to Dimension Theory and Dynamical Systems; Chapter 5. Dimension of Cantor-like Sets and Symbolic Dynamics; Chapter 6. Multifractal Formalism; Chapter 7. Dimension of Sets and Measures Invariant Under Hyperbolic Systems; Appendix IV: A General Concept of Multifractal Spectra; M.
Series Title: Chicago lectures in mathematics.

Abstract:

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 invar.

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