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Is Trivial Dynamics That Trivial?
- Source :
- American Mathematical Monthly; Feb2006, Vol. 113 Issue 2, p109-133, 25p, 11 Graphs
- Publication Year :
- 2006
-
Abstract
- The article explores the theory of dynamical systems in mathematics, examining the papers of A. N. Sharkovsky and T.-Y. Li and J. A. Yorke on interval dynamics, among others. It should be noted that neither Sharkovsky's theorem nor Li-Yorke's definition of chaos have a significant role in the core of modern one-dimensional dynamics. Meanwhile, J. Guckenheimer's paper established the foundations for the almost everywhere approach to dynamics, which states that if a map is sufficiently smooth, there may be a fair chance of offering an effective description of the asymptotic behavior of almost every point of the interval.
Details
- Language :
- English
- ISSN :
- 00029890
- Volume :
- 113
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- American Mathematical Monthly
- Publication Type :
- Academic Journal
- Accession number :
- 20096888
- Full Text :
- https://doi.org/10.1080/00029890.2006.11920286