Resumen
In a previous paper (Ciklová 2006 Nonlinearity 19 517–29 ) a family of minimal, Li–Yorke sensitive dynamical systems (X, T) without weak mixing factors has been constructed, disproving a conjecture by Akin and Kolyada (2003 Nonlinearity 16 1421–33 ). In this article we show that, in addition, any system in the above-mentioned family has an almost one-to-one minimal extension which fails to be Li–Yorke sensitive. This disproves another conjecture by Akin and Kolyada.