weakly unimodal map; arc-like; Li-Yorke chaotic; indecomposable continuum; zero topological entropy

We show that for every positive integer k there exists an interval map f:I?I such that (1) f is Li-Yorke chaotic, (2) the inverse limit space I_f=lim?{f,I} does not contain an indecomposable subcontinuum, (3) f is C^k-smooth, and (4) f is not C^(k+1)-smooth. We also show that there exists a C^?-smooth f that satisfies (1) and (2). This answers a recent question of Oprocha and the first author from (Proc. Am. Math. Soc. 143(8):3659-3670, 2015), where the result was proved for k=0. Our study builds on the work of Misiurewicz and Smítal of a family of zero entropy weakly unimodal maps. Some results on the structure of this continua are also mentioned. Finally, we prove that the chaotic attractors we construct are topologically distinct from the one presented by P. Oprocha and the first author.