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Study "Chaotic evolution and strange attractors" by D. Ruelle
Posted on 2010-03-16
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More "Chaotic evolution and strange attractors" by D. Ruelle The statistical analysis of time series for deterministic nonlinear systems. Series: Lezioni Lincee This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. • | • This review collects together a series of lectures given by David Ruelle at the Accademia dei Lincee (Rome, May, 1987) and deals with those aspects of dynamical systems which are more closely related with ergodic theory, namely with the study of the properties of the invariant measures generated by the time evolutions themselves. Contents Foreword Introduction Part I. Steps to a Deterministic Interpretation of Chaotic Signals: 1. Descriptions of turbulence 2. A bit more on turbulence 3. The Hénon mapping 4. Capacity and Hausdorff dimension 5. Attracting sets and attractors 6. Extracting geometric information from a times series Part II. The Ergodic Theory of Chaos: 7. Invariant probability measures 8. Physical measures 9. Characteristic exponents 10. Invariant manifolds 11. Axiom A and structural stability 12. Entropy 13. Dimensions 14. Resonances 15. Conclusions References Bibliography Index.
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