Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 7, 2018 https://doi.org/10.1007/s10114-018-6485-3 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications Elias ABBOUD The Academic Arab Institute, Faculty of Education, Beit Berl College, Doar Beit Berl 44905,Israel E-mail : email@example.com Abstract In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and greatest words. In particular, we characterize all the cases for which β β = β β where β and β are the 1 1 2 2 1 2 greatest words in β and β of M (n). 1 2 Keywords Word equation, broken alternating word, primitive word, greatest word, parity-lexicograp- hic order MR(2010) Subject Classiﬁcation 68R15, 37B10, 05A99 1 Introduction Words in discrete dynamical systems have been widely studied. Sun and Helmberg  pre- sented an algorithm for recognizing maximality of a word by introducing an extended order of words connected with unimodal maps. Chen and Wang  studied the relation between the kneading sequences
Acta Mathematica Sinica, English Series – Springer Journals
Published: May 7, 2018
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