| Contents |
| We show that for every positive integer $k$ there exists an interval map $f:I\to I$ such that:
(1) $f$ is Li-Yorke chaotic,
(2) the inverse limit space $\lim_{\leftarrow}\{f,I\}$ 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 $C^\infty$-smooth $f$ that satisfies (1)-(2). This answers a recent question of P. Oprocha and J. P. Boronski from [\emph{On indecomposability in chaotic attractors}, preprint 2013], where the result was proved for $k=0$. |
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