Date:

Tue, 17/05/202214:00-15:00

**Abstract**. A hypercubic billiard word – or cubic billiard word in dimension d – is a word on the d-letter alphabet denoting the sequence of the faces successively hit by a billiard ball moving in the unit cube of R^d, in which two parallel faces are encoded by the same letter. The imbalance of a word w is the maximal difference [possibly infinite] in the number of occurrences of a letter in two subwords of same length of w. We know from the work of Morse and Hedlund (1940) that square billiard words generated by a momentum with rationally independant entries are exactly binary aperiodic words with imbalance equal to 1 (also known as Sturmian words). Vuillon (2003) showed that cubic billiard words whose momentum has rationally independant entries in dimension d have imbalance lower or equal to d − 1. In this talk, I will completely describe the imbalances of this class of words.

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