1 |
S. Ferenczi and C. Mauduit, Transcendence of numbers with a low complexity expansion, J. Number Theory 67 (1997), no. 2, 146-161.
DOI
ScienceOn
|
2 |
L. Flatto, Z-numbers and -transformations, Symbolic dynamics and its applications (New Haven, CT, 1991), 181-201, Contemp. Math., 135, Amer. Math. Soc., Providence, RI, 1992.
|
3 |
L. Flatto, J. C. Lagarias, and A. D. Pollington, On the range of fractional parts {}, Acta Arith. 70 (1995), no. 2, 125-147.
DOI
|
4 |
D. Y. Kwon, A devil's staircase from rotations and irrationality measures for Liouville numbers, Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 3, 739-756.
|
5 |
D. Y. Kwon, A two dimensional singular function via Sturmian words in base , preprint (2011). Available at http://www.math.jnu.ac.kr/doyong/paper/twosing_Apr2011.pdf
|
6 |
M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 2002.
|
7 |
K. Mahler, An unsolved problem on the powers of 3/2, J. Austral. Math. Soc. 8 (1968), 313-321.
DOI
|
8 |
M. Morse and G. A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. 62 (1940), 1-42.
DOI
ScienceOn
|
9 |
W. Parry, On the -expansion of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401-416.
DOI
|
10 |
A. Renyi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8 (1957), 477-493.
DOI
|
11 |
J. Berstel, A. Lauve, C. Reutenauer, and F. V. Saliola, Combinatorics on Words, American Mathematical Society, 2009.
|
12 |
B. Adamczewski and Y. Bugeaud, On the complexity of algebraic numbers. I. Expansions in integer bases, Ann. of Math. (2) 165 (2007), no. 2, 547-565.
DOI
|
13 |
J.-P. Allouche and A. Glen, Distribution modulo 1 and the lexicographic world, Ann. Sci. Math. Quebec 33 (2009), no. 2, 125-143.
|
14 |
J.-P. Allouche and A. Glen, Extremal properties of (epi)Sturmian sequences and distribution modulo 1, Enseign. Math. (2) 56 (2010), no. 3-4, 365-401.
DOI
ScienceOn
|
15 |
F. Blanchard, -expansions and symbolic dynamics, Theoret. Comput. Sci. 65 (1989), no. 2, 131-141.
DOI
ScienceOn
|
16 |
Y. Bugeaud and A. Dubickas, Fractional parts of powers and Sturmian words, C. R. Math. Acad. Sci. Paris 341 (2005), no. 2, 69-74.
DOI
ScienceOn
|
17 |
S. Bullett and P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase, Math. Proc. Cambridge Philos. Soc. 115 (1994), no. 3, 451-481.
DOI
|
18 |
E. M. Coven and G. A. Hedlund, Sequences with minimal block growth, Math. Systems Theory 7 (1973), 138-153.
DOI
|
19 |
D. P. Chi and D. Y. Kwon, Sturmian words, -shifts, and transcendence, Theoret. Comput. Sci. 321 (2004), no. 2-3, 395-404.
DOI
ScienceOn
|