The main result of this talk states, that for a continuous interval map $f$, the set of all Li-Yorke chaotic pairs which are not distributionally chaotic (of any type) is always of the first category in $I \times I$. This result has several immediate applications. For example, the characterization of generic Li-Yorke chaos by Snoha in [1] is valid also for distributional chaos. Following Geschke et al. in [2] we can deduce, that the existence of an uncountable $DCi$ scrambled set implies the existence of a Cantor $DCi$ scrambled set for the interval map $f$, where $i=1,2,3$.

[1] L. Snoha; Generic chaos, Comment. Math. Univ. Carol., Vol. 31 (1990), No. 4, 793-810.

[2] S. Geschke, J. Grebík, B. D. Miller; Scrambled Cantor sets, Proceedings of AMS, Vol.149, 10 (2021).