On balanced sequences and their critical exponent

We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is fully characterised by a Sturmian u and two constant gap y y′. show that the language eventually dendric we focus on return words to its factors. develop method for computing critical exponent asymptotic sequences, provided associated has quadratic slope. The based looking shortest bispecial factors in v. illustrate our several examples; particular confirm conjecture Rampersad, Shallit Vandomme specific have least among all 9-letter (resp., 10-letter)