Palindromic factors of billiard words

We study palindromic factors of billiard words, in any dimension. There are differences between the two-dimensional case, and higher dimension. Arbitrary long palindrome factors exist in any dimension, but arbitrary long palindromic prefixes exist in general only in dimension 2.

[1]  Laurent Vuillon,et al.  A Characterization of Sturmian Words by Return Words , 2001, Eur. J. Comb..

[2]  Xavier Droubay,et al.  Palindromes in the Fibonacci Word , 1995, Inf. Process. Lett..

[3]  M. Lothaire.  Algebraic Combinatorics on Words , 2002 .

[4]  Mukarram Ahmad,et al.  Continued fractions , 2019, Quadratic Number Theory.

[5]  Pierre Arnoux,et al.  Complexity of sequences defined by billiard in the cube , 1994 .

[6]  Aldo de Luca,et al.  Combinatories of Standard Sturmian Words , 1997, Structures in Logic and Computer Science.

[7]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[8]  Giuseppe Pirillo,et al.  Palindromes and Sturmian Words , 1999, Theor. Comput. Sci..

[9]  Aldo de Luca,et al.  Sturmian Words: Structure, Combinatorics, and Their Arithmetics , 1997, Theor. Comput. Sci..

[10]  Baryshnikov,et al.  Complexity of trajectories in rectangular billiards , 1994, chao-dyn/9406001.

[11]  Aldo de Luca,et al.  Sturmian Words, Lyndon Words and Trees , 1997, Theor. Comput. Sci..

[12]  Jean-Pierre Borel,et al.  Quelques mots sur la droite projective réelle , 1993 .