ACCUEIL 

RESEARCH

ENSEIGNEMENT  


Member of:

GDR IM ; ANR IZES

 Topic of research

Dynamical systems and more specifically: geometrical  theory of dynamical systems, ergodic theory, symbolic dynamics, lamination, tilings,...

 Publications

  1. S. Petite.  On invariant measures of finite affine type tilings,  Ergod. Th. & Dynam. Sys. 26 (2006), no 4, 1159--1176.pdf

  2. J.M. Gambaudo , P. Guiraud, S. Petite. Minimal configurations for Frenkel-Kontorova model on a quasicrystal Comm. in Math.Phys.  265, (2006), no 1, 165--188   .pdf

  3. M.I. Cortez, S. Petite. $G$-odometers and their almost 1-1 extensions.  J. Lond. Math. Society, 78, (2008), no 1, 1--20. pdf

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

  5. H. Oyono-Oyono, S. Petite. C^*-algebras of Penrose hyperbolic tilings.   Journal of Geometry and Physics61 (2011), pp. 400--424.   .pdf

  6. M.I. Cortez, S. Petite.  Invariant measures and orbit equivalence for generalized Toeplitz subshiftsGroups, Geometry, and Dynamics. 8 (2014) no. 4., 1007--1045   .pdf

  7. E. Garibaldi, S. Petite, P. Thieullen. Discrete weak-KAM methods for stationary uniquely ergodic settingAnn. Henri Poincaré 18 (2017), no. 9, 2905--2943. .pdf

  8. J. Aliste-Prieto, S. Petite. On the simplicity of homeomorphisms groups of a tilable laminationMonatsh. Math.  181 (2016), no. 2,  285--300. .pdf

  9. M.I. Cortez, F. Durand, S. Petite. Eigenvalues and strong orbit equivalenceErgod. Th. & Dynam. Sys.  36 (2016), no. 8, 2419--2440 .pdf

  10. F. Durand, S. Petite. Conjugacy of Unimodular Pisot Substitution Subshifts to Domain Exchanges, To appear in AHL 30 p. .pdf

  11. S. Donoso, F. Durand, A. Maass, S. Petite. On automorphism groups of low complexity minimal subshifts, Ergod. Th. & Dynam. Sys. 36 (2016), no 1, 64--95 .pdf
     
  12. Y. Fares, S. Petite. The valuative capacity of subshifts of finite type, Journal of Number theory  158 (2016); 165-184  .pdf

  13. F. Durand, N. Ormes, S. Petite. Self-Induced Systems   J.Anal. Math. 135 (2018), no. 2, 725--756.  .pdf

  14. V. Cyr, J. Franks, B. Kra, S. Petite. Distortion and the automorphism group of a shift. Journal of Modern Dynamics (2018), 13,  147--161. .pdf

  15. S. Donoso, F. Durand, A. Maass, S. Petite. On automorphism groups of Toeplitz subshifts. Discrete Analysis 2017:11, 19 pp..pdf

  16. M.I. Cortez, S. Petite.  Realization of big centralizers of minimal aperiodic actions on the Cantor set Disc. & Cont. Dyn. Systs A (2020), 40 (5),  2891--2901..pdf

  17. V. Berthé , P. Cecchi,  F. Durand, J. Leroy, D. Perrin, S. Petite On the dimension group of unimodular S-adic subshifts.  Monatsh. Math. 194 (2021), no. 4, 68--71  .pdf

  18. S. Donoso, F. Durand, A. Maass, S. Petite. Interplay between finite topological rank minimal Cantor systems, S-adic subshifts and their complexity  Trans. Amer. Math. Soc. 374 (2021), no. 5, 3453--3489. .pdf

  19. E. Garibaldi, S. Petite, P. ThieullenClassification of discrete weak KAM solutions on linearly repetitive quasi-periodic sets Comm. Math. Phys. 405 (2024), no. 12, Paper No. 291 .pdf

  20. C. Cabezas, S. Petite. Large normalizers of Zd-odometers systems and realization on substitutive subshifts  Discrete & Contin. Dyn. Syst. A (2024), 44 (12), 3848–3877 .pdf

  21. S. Donoso, A. Maass, S. Petite. A geometric framework for asymptoticity and expansivity in topological dynamics Trans. Amer. Math. Soc. 377 (2024), no. 12, 8935–8961..pdf

  22. V. Cyr, B. Kra, S. Petite. Strong Approximations of Shifts and the Characteristic Measures Problem  Math. Z. 309 (2025), no. 1, Paper No. 1 .pdf
     

Book Chapter
  • J. Aliste-Prieto, D. Coronel, M.I. Cortez, F. Durand, S. Petite. "Linearly repetitive Delone sets"
    dans  J. Kellendonk, D. Lenz, J. Savinien (eds),  Mathematics of Aperiodic Order, Birkhäuser, Progress in Mathematics, (309) 2015 pp 195--222   .pdf

  • S. Petite "Automorphismes de sous-shifts minimaux" .pdf

PhD Thesis

Tilings of the hyperbolic half-plane and laminations  .pdf (In french)

Ph.d. Advisor : Pr J-M  Gambaudo, Université de Bourgogne
Defense: October the 24
th   2005 at Dijon (Institut de Mathématiques de Bourgogne)

H.D.R. Habilitation à diriger des recherches

Actions on a Cantor set. From symbolic dynamics to quasicrystals  .pdf (in french)  Long version .pdf

Defense: November the 30th  2015 at Amiens (Laboratoire Amiénois de Mathématique Fondamentale et Appliquée)

Miscellaneous

A dynamical approach of Delone sets and tilings : lecture notes  .pdf

Lectures on the automorphism group of subshifts: .pdf1   .pdf2  .pdf3