2010/08/25 by Karma Dajani, Dajani, Karma, Charlene Kalle +1
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1008.4289
We introduce a family of dynamical systems that generate negative\n\β-expansions and study the support of the invariant measure which is\nabsolutely continuous with respect to Lebesgue measure. We give a\ncharacterization of the set of digit sequences that is produced by a typical\nmember of this family of transformations. We discuss the meaning of greedy\nexpansions in the negative sense, and show that there is no transformation in\nthe introduced family of dynamical systems that generates negative greedy.\nHowever, if one looks at random algorithms, then it is possible to define a\ngreedy expansion in base -\β.\n