On variants of distributional chaos in dimension one

摘要

In their famous paper from 1994, B. Schwaizer and J. Smital, [B. Schwaizer and J. Smital, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), pp. 737-754] fully characterized topological entropy of interval maps in terms of distribution functions of distance between trajectories. Strictly speaking, they proved that a continuous map ?: [0,1] → [0,1] has zero topological entropy if and only if for every x, y e [0,1] the following limit exists:lim -{0