Bispecial Factors in the Brun S-Adic System

We study the bispecial factors in the S-adic system associated with the Brun Multidimensional Continued Fraction algorithm. More precisely, by describing how strong and weak bispecial words can appear, we get a sub-language of the Brun language for which all bispecial words are neutral.

[1]  Fabien Durand,et al.  Corrigendum and addendum to ‘Linearly recurrent subshifts have a finite number of non-periodic factors’ , 2003, Ergodic Theory and Dynamical Systems.

[2]  Vincent Delecroix,et al.  Balancedness of Arnoux-Rauzy and Brun Words , 2013, WORDS.

[3]  Gérard Rauzy,et al.  Représentation géométrique de suites de complexité $2n+1$ , 1991 .

[4]  Karel Klouda,et al.  Bispecial factors in circular non-pushy D0L languages , 2012, Theor. Comput. Sci..

[5]  G. A. Hedlund,et al.  Symbolic Dynamics II. Sturmian Trajectories , 1940 .

[6]  Jérémie Bourdon,et al.  A combinatorial approach to products of Pisot substitutions , 2014, Ergodic Theory and Dynamical Systems.

[7]  A. Brentjes,et al.  A two-dimensional continued fraction algorithm for best approximations with an application in cubic number fields. , 1981 .

[8]  Valérie Berthé,et al.  On the Pisot Substitution Conjecture , 2015 .

[9]  B. R. Schratzberger,et al.  The Quality of Approximation of Brun’s Algorithm in Three Dimensions , 2001 .

[10]  Valérie Berthé Combinatorics , Automata and Number Theory , 2011 .

[11]  Valérie Berthé,et al.  Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm , 2014, Adv. Appl. Math..

[12]  Jeffrey C. Lagarias,et al.  The quality of the Diophantine approximations found by the Jacobi-Perron algorithm and related algorithms , 1993 .

[13]  Fritz Schweiger,et al.  Multidimensional continued fractions , 2000 .

[14]  Wolfgang Steiner,et al.  Geometry, dynamics, and arithmetic of $S$-adic shifts , 2014, Annales de l'Institut Fourier.

[15]  G. Rauzy Nombres algébriques et substitutions , 1982 .