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Introduction to the Modern Theory of Dynamical Systems
Abstract
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
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Cited by
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Lind, D., & Marcus, B. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108899727 · Cited by 2,696
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
Time series forecasting for nonlinear and non-stationary processes: a review and comparative study
Cheng, C., Sa-Ngasoongsong, A., Beyca, O., Le, T., Yang, H., Kong, Z. (., & Bukkapatnam, S. T. S. (2015) · IIE Transactions · doi:10.1080/0740817x.2014.999180 · Cited by 287
On the measure of maximal entropy for finite horizon Sinai Billiard maps
Baladi, V., & Demers, M. (2020) · Journal of the American Mathematical Society · doi:10.1090/jams/939 · Cited by 31
Metadata
- Authors
- Katok, A., & Hasselblatt, B.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1995-04-28
- OpenAlex
- W4212958445
- Cited by
- 2,169
- References
- 0
- FWCI
- 3.19
- Type
- book
- Language
- en
- Open access
- closed
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- Katok, A., & Hasselblatt, B. (1995). Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press eBooks. https://doi.org/10.1017/cbo9780511809187
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
