Mirror substitutions and palindromic sequences

By introducing the notion of mirror substitution, we show that, given a substitutive sequence over two letters, it is palindromic (that is, it contains arbitrarily long palindromes) if and only if its language is mirror-invariant (that is, it is closed under the mirror image map). Then we solve a question of Hof, Knill and Simon in the 2-letter case, and also, by constructing a counterexample, we give a negative answer to the open problem 4 in the webpage: http://iml.univ-mrs.fr/~bernat/openquestions.html.