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Introduction to the modern theory of dynamical systems
Abstract
Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.
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Cited by
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Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00137-0 · Cited by 2,764
Baptista, M. S. (1998) · Physics Letters A · doi:10.1016/s0375-9601(98)00086-3 · Cited by 885
Extracting macroscopic dynamics: model problems and algorithms
Givon, D., Kupferman, R., & Stuart, A. (2004) · Nonlinearity · doi:10.1088/0951-7715/17/6/r01 · Cited by 363
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VISWANATH, D. (2007) · Journal of Fluid Mechanics · doi:10.1017/s0022112007005459 · Cited by 293
Food for Thought … Mechanistic Validation
Hartung, T. (2013) · ALTEX · doi:10.14573/altex.2013.2.119 · Cited by 93
Metadata
- Venue
- Choice Reviews Online
- Publisher
- American Library Association
- Published
- 1996-06-01
- Volume
- 33
- Issue
- 10
- Pages
- 33-5770-33-5770
- ISSN
- 0009-4978 (ISSN-L)
- 1523-8253
- OpenAlex
- W2081817659
- Cited by
- 3,592
- References
- 0
- Type
- book review
- Language
- en
- Open access
- closed
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