Publications


29) On Cobham's theorem, F. Durand et M. Rigo, Chapter in Automata: from Mathematics to Applications, European Mathematical Society, Editor J.-É. Pin, preprint (.pdf) .

28) HD0L $\omega$-equivalence and periodicity problems in the primitive case (to the memory of G. Rauzy), J. of Uniform Distribution Theory 7 (2012), 199-215.

27) Cobham's theorem for substitutions, F. Durand, J. Eur. Math. Soc. 13 (2011), 1797–1812. (.pdf)

26) Boundary of the Rauzy fractal set in $\RR \times \CC$ generated by $P(x) = x^4-x^3-x^2-x-1$, F. Durand et A. Messaoudi, Osaka J. of Math. 48 (2011), 471-496. (.pdf)

25) Combinatorics on Bratteli diagrams and dynamical systems, Combinatorics, Automata and Number Theory, Series Encyclopedia of Mathematics and its applications 135, Cambridge University Press 2010, 338-386. (.pdf)

24)  Linearly repetitive Delone systems have a finite number of non periodic Delone system  factors, M. I. Cortez, F. Durand et S. Petite, Proc. Amer. Math. Soc. 138 (2010), 1033-1046. (.pdf)

23) Eigenvalues of finite rank Bratteli-Vershik dynamical systems, X. Bressaud, F. Durand et  A. Maass, Ergod. Th. & Dynam. Sys. 30 (2010), 639–664.

22) Minimal polynomial dynamics on the set of 3-adic integers, F. Durand et F. Paccaut, Bull. of the London Math. Soc. 41 (2009), 302-314. (.pdf)

21) Syndeticity and independent substitutions, F. Durand et M. Rigo, Adv. in Applied Math.  42 (2009), 1-22. (.pdf)

20)  Self-similar tiling systems, topological factors and stretching factors, M. I. Cortez et F. Durand, Disc. and Comp. Geometry 40 (2008), 622-640. (.pdf)

19) Cobham-Semenov theorem and $\NN^d$-subshifts, F. Durand, Theo. Comp. Sc. 391 (2008), 20-38. (.pdf)

18 ) Necessary and sufficient conditions  to be an eigenvalue for linearly recurrent dynamical Cantor systems, X. Bressaud, F. Durand et  A. Maass,  Journal of the London Mathematical Society  72 (2005), 799-816. (.pdf)

17) Local rates of Poincaré recurrence for rotations and weak mixing,  J.-R. Chazottes et F. Durand, Discrete and Continuous Dynamical Systems  12 (2005)  175 - 183. (.pdf)

16) Words and morphisms with Sturmian erasures, F. Durand, A. Guerziz et M. Koskas,  Bulletin of the Belgian Mathematical Society 11 (2004), 575-588. (.pdf)

Habilitation à diriger des recherches : Récurrence en Dynamique Topologique d'Entropie Nulle, soutenue  le  lundi 15 novembre 2004 à l'Université de Picardie Jules Verne (version longue et courte).

15) Substitution dynamical systems and countable scrambled sets, F. Blanchard, F. Durand et  A. Maass,  Nonlinearity 17 (2004), 817-833. (.pdf)

14 ) Continuous and measurable eigenfunctions of linearly recurrent dynamical Cantor systems, M. I. Cortez, F. Durand, B. Host et  A. Maass,  Journal of the London Mathematical Society 67 (2003), 790-804. (.pdf)

13 ) Corrigendum and addendum to: Linearly recurrent subshifts have a finite number of non-periodic factors, F. Durand,  Ergod. Th. & Dynam. Sys. 23 (2003), 663-669. (.pdf)

12 ) A note on limit laws for minimal Cantor systems with infinite periodic spectrum, F. Durand et A. Maass,  Discrete and Continuous Dynamical Systems  9 (2003), 745-750. (.pdf)

11 ) A Theorem of Cobham for non primitive substitutions, F. Durand, Acta Arithmetica  104 (2002), 225--241. (.pdf)

10 ) Factors of Toeplitz flows and other almost 1-1 extensions over group rotations, T. Downarowicz et F. Durand, Math. Scand. 90 (2002), 57--72. (.pdf)

9 )  Combinatorial and Dynamical study of substitutions around the Theorem of Cobham, F. Durand, Dynamics and Randomness, Nonlinear Phenomena and Complex Systems, Kluwer Acad. Pub, 2002,   53 -- 94. (.pdf)

8 ) Ergodic averages with deterministic weights, F. Durand et D. Schneider , Annales de l'Institut Fourier 52 (2002),  559--581. (.pdf)

7 )  Limit laws of entrance times for low complexity Cantor minimal systems, F. Durand et A. Maass , Nonlinearity 14 (2001),  683--700. (.pdf)

6 )  Orbit equivalence for sturmian subshifts, P. Dartnell, F. Durand et A. Maass , Studia Math. 142 (2000),  25--45. (.pdf)

5)  Linearly recurrent subshifts have a finite number of non-periodic subshift factors, F. Durand, Ergod. Th. & Dynam. Sys. 20 (2000), 1061--1078. (.pdf)

4)  Substitution dynamical systems, Bratteli diagrams and dimension groups, F. Durand, B. Host et C. Skau, Ergod. Th. & Dynam. Sys. 19 (1999), 953--993. (.pdf)

3)  Sur les ensembles d'entiers reconnaissables, F. Durand,  J. de Théorie des Nombres de Bordeaux 10 (1998), 65--84. (.pdf)

2)  A generalization of Cobham's theorem, F. Durand, Theory of Computing Systems 31 (1998), 169--185. (.pdf)

1)  A characterization of substitutive sequences using return words, F. Durand, Discrete Mathematics 179 (1998), 89--101. (.pdf)

0)  Contributions à l'étude des suites et systèmes dynamiques substitutifs. Thèse (1996), Université de la Méditerranée (Aix-Marseille II). (.pdf)