Eulerian entropy and non-repetitive subword complexity

Measuring Complexity in Cantor Dynamics

“…The exact relationships among h E (X, T, x), h E (X, T ), and h top (X, T ) are not clear, but here are some results from [143].…”

“…How about a definition in Z d ? 3.9 Nonrepetitive complexity and Eulerian entropy T. K. S. Moothathu [143] defined the nonrepetitive complexity function P N u of a sequence u on a finite alphabet A in terms of how long an initial block of u could be before it contained a repeat of a subblock of length n:…”

Initial nonrepetitive complexity of regular episturmian words and their Diophantine exponents

“…The notion of initial nonrepetitive complexity was introduced independently by Moothatu [28] and Bugeaud and Kim [13]. Nicholson and Rampersad [29] examine the general properties of this function and determine it explicitly for certain words such as the Thue-Morse word, the Fibonacci word, and the Tribonacci word.…”

On non-repetitive complexity of Arnoux-Rauzy words

“…A dual function to R u was recently introduced by Moothathu [13] under the name non-repetitive complexity function nrC u . The value nrC u (n) is defined as the maximal m such that for some i ∈ N any factor of u of length n occurs at most once in u i u i+1 u i+2 • • • u i+m+n−2 .…”