Complexity of sequences and dynamical systems

Discrete Mathematics

Volumn 206, Issue 1-3, 1999, Pages 145-154

  Ferenczi, Sébastien ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012005928     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(98)00400-2     Document Type: Article

References (32)

1. P. Alessandri, Codages de rotations et basses complexités, Ph.D. Thesis, University Aix-Marseille 2, 1996.
2. J.-P. Allouche, Sur la complexité des suites infinies, Bull. Belg. Math. Soc. 1 (2) (1994) 133-143.
3. P. Arnoux, C. Mauduit, I. Shiokawa, J.-I. Tamura, Complexity of sequences defined by billiards in the cube, Bull. Soc. Math. France 122 (1994) 1-12.
4. P. Arnoux, G. Rauzy, Représentation géométrique de suites de complexité 2n + 1, Bull. Soc. Math. France 119 (1991) 199-215.
5. Yu. Baryshnikov, Complexity of trajectories in rectangular billiards, Commun. Math. Phys. 174 (1995) 43-56.
6. G. Blanc, N. Bleuzen-Guernalec, Production en temps réel et complexité de structures de suites infinies, Inform. Théori. Appl. RAIRO 23 (1989) 195-216.
7. F. Blanchard, B. Host, A. Maass, Topological Complexity, Institut de Mathématiques de Luminy (1998) preprint.
8. F. Blanchard, P. Kůrka, Language complexity of rotations and Sturmian sequences, Theoret. Comput. Sci. 209 (1998) 179-193.
9. M. Boshernitzan, Unique ergodicity of minimal symbolic flows with linear block growth, J. Anal. Math. 44 (1985) 77-96.
10. M. Boshernitzan, A condition for unique ergodicity of minimal symbolic flows, Ergodic Theory Dyn. Systems 12 (1992) 425-428.
11. S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Appl. Math. 24 (1989) 83-96.
12. J. Cassaigne, Special factors of sequences with linear subword complexity, Developments in Language Theory, World Scientific, Singapore, 1996, pp. 25-34.
13. J. Cassaigne, Complexité et facteurs spéciaux, Bull. Belg. Math. Soc. 4 (1997) 67-88.
14. J. Cassaigne, J. Karhumaki, Toeplitz words, generalized periodicity and periodically iterated morphisms, Eur. J. Combin. 18 (1997) 497-510.
15. A. Cobham, Uniform tag sequences, Math. Systems Theory 6 (1972) 164-192.
16. A. de Luca, S. Varrichio, Some combinatorial properties of the Thue-Morse sequence, Theoret. Comput. Sci. 63 (1989) 333-348.
17. F. Durand, Contribution à l'étude des suites et systèmes dynamiques substitutifs, Ph.D. Thesis, University Aix-Marseille 2, 1996.
18. F. Durand, A characterization of substitutive sequences using return words, Discrete Math. 179 (1998) 89-101.
19. A. Ehrenfeucht, K.P. Lee, G. Rozenberg, Subword complexities of various classes of deterministic developmental languages without interactions, Theoret. Comput. Sci. 1 (1975) 59-75.
20. S. Ferenczi, Les transformations de Chacon: combinatoire, structure géométrique, liens avec les systèmes de complexité 2n + 1, Bull. Soc. Math. France 123 (1995) 271-292.
21. S. Ferenczi, Rank and symbolic complexity, Ergodic Theory Dyn. Systems 16 (1996) 663-682.
22. S. Ferenczi, Measure-theoretic complexity of ergodic systems, Israel J. Math. 100 (1997) 189-207.
23. S. Ferenczi, C. Mauduit, Transcendence of numbers with a low complexity expansion, J. Number Theory 67 (1997) 146-161.
24. J. Goyon, Construction de suites dont la complexité a un ordre de grandeur donné, Institut de Mathématiques de Luminy (1997) preprint.
25. C. Grillenberger, Construction of strictly ergodic systems I. Given entropy, Z. Wahrscheinlichkeitstheorie verw. Geb. 25 (1973) 323-334.
26. G.A. Hedlund, M. Morse, Symbolic dynamics, Amer. J. Math. 60 (1938) 815-866.
27. G.A. Hedlund, M. Morse, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. 62 (1940) 1-42.
28. M. Koskas, Complexités de suites de Toeplitz, Discrete Math. 183 (1998) 161-183.
29. M. Li, P. Vitányi, Kolmogorov complexity and its applications, Handbook of Theoretical Computer Science, vol. A: Algorithms and Complexity, MIT Press, Cambridge, 1990, pp. 187-254.
30. J.-J. Pansiot, Complexité des facteurs des mots infinis enegendrés par morphismes itérés, in: ICALP '84, Lecture Notes in Computer Science, vol. 172, Springer, Berlin, 1984, pp. 380-389.
31. M. Queffelec, Substitution dynamical systems - Spectral analysis, Lecture Notes in Mathematics, vol. 1294, Springer, Berlin, 1987.
32. G. Rauzy, Echanges d'intervalles et transformations induites, Acta Arith. 34 (1979) 315-328.