Is Trivial Dynamics That Trivial?

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.