# On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications

On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps... 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 : eabboud@beitberl.ac.il 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 [8] pre- sented an algorithm for recognizing maximality of a word by introducing an extended order of words connected with unimodal maps. Chen and Wang [5] studied the relation between the kneading sequences http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

# On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications

, Volume OnlineFirst – May 7, 2018
14 pages

/lp/springer_journal/on-word-equations-originated-from-discrete-dynamical-systems-related-BXr8T1rOaz
Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-018-6485-3
Publisher site
See Article on Publisher Site

### Abstract

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 : eabboud@beitberl.ac.il 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 [8] pre- sented an algorithm for recognizing maximality of a word by introducing an extended order of words connected with unimodal maps. Chen and Wang [5] studied the relation between the kneading sequences

### Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 7, 2018

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