Th¨¨mes de Recherche

Syst¨¨mes dynamiques et Th¨¦orie ergodique Th¨¦orie m¨¦trique des nombres Approximation diophantienne Multifractals Probabilit¨¦s Analyse harmonique

Th¨¨se

Études sur la R¨¦currence de Certains Syst¨¨mes Dynamiques Topologiques et Arithm¨¦tiques, 198 pages.
Soutenue : le 20 mai 2008 Tr¨¨s Honorable,
Directeur : Ai-Hua FAN; Pr¨¦sident: Jean-Pierre KAHANE; Rapporteurs: Yann BUGEAUD, Jörg SCHMELING; Examinateurs: Jean-Luc CHABERT, Fabien DURAND, Bernard HOST.

Habilitation ¨¤ Diriger des Recherches

Diff¨¦rents aspects de syst¨¨mes dynamiques r¨¦els et $p$-adiques,
Soutenue : le 12 d¨¦cembre 2017.
Pr¨¦sident : Pierre ARNOUX; Rapporteurs : Julien BARRAL, Charles FAVRE, Mark POLLICOTT; Examinateurs : Val¨¦rie BERTHÉ, Yann BUGEAUD, St¨¦phane SEURET.

Publications

Analyse multifractale des syst¨¨mes dynamiques, th¨¦orie m¨¦trique des nombres, approximation Diophantienne :

  1. Generic points in systems of specification and Banach valued Birkhoff ergodic average, Discrete Contin. Dyn. Syst., 21 (2008) 1103-1128, (with Ai-Hua Fan and Jacques Peyri¨¨re) arXiv
  2. Dimension of some non-normal continued fraction sets, Math. Proc. Camb. Phil. Soc., 145 (2008), no. 1, 215-225, (with Ji-Hua Ma and Bao-Wei Wang) PDF
  3. On Khintchine exponents and Lyapunov exponents of continued fractions, Ergodic Theory and Dynamical Systems, 29 (2009), 73-109, (with Ai-Hua Fan, Bao-Wei Wang and Jun Wu) arXiv
  4. On the frequency of partial quotients of regular continued fractions, Math. Proc. Camb. Phil. Soc., 148 (2010), 179-192, (with Ai-Hua Fan and Ji-Hua Ma) arXiv
  5. Dimension of Besicovitch-Eggleston sets in the countable symbolic space, Nonlinearity, 23 (2010) 1185-1197, (with Ai-Hua Fan, Ji-Hua Ma and Bao-Wei Wang) PDF
  6. Level sets of multiple ergodic averages, Monatshefte f¨¹r Mathematik, 168, no. 1, (2012), 17-26, (with Ai-Hua Fan and Ji-Hua Ma) arXiv
  7. Diophantine approximation by orbits of expanding Markov maps, Ergodic Theory and Dynamical Systems, 33, no. 2, (2013), 585-608, (with St¨¦phane Seuret) arXiv
  8. Inhomogeneous Diophantine approximation with general error functions, Acta Arith., 160 (2013), 25-35, (with Michał Rams) arXiv
  9. Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents, Real Analysis Exchange, 39, no. 1(2013), 1-14, (with Michał Rams) arXiv
  10. On the fast Khintchine spectrum in continued fractions, Monatshefte f¨¹r Mathematik, 171(2013), 329-340, (with Ai-Hua Fan, Bao-Wei Wang and Jun Wu) arXiv
  11. Multifractal analysis for expanding interval maps with infinitely many branches, Trans. Amer. Math. Soc. 367 (2015), 1847-1870, (with Ai-Hua Fan, Thomas Jordan, and Michał Rams) arXiv
  12. Uniform Diophantine approximation related to $b$-ary and $\beta$-expansions, Ergodic Theory and Dynamical Systems, 36, no. 1, (2016), 1-22, (with Yann Bugeaud) arXiv
  13. Subexponentially increasing sum of partial quotients in continued fraction expansions, Math. Proc. Camb. Phil. Soc., 160 (2016), 401-412, (with Michał Rams) arXiv
  14. Upper and lower fast Khintchine spectra in continued fractions, Monatshefte f¨¹r Mathematik, 180 (2016), 65-81, (with Michał Rams) arXiv
  15. Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential, Fractals, Vol. 26, No. 3 (2018) 1850026 (13 pages), (with Dong Han Kim, Michał Rams and Bao-Wei Wang) arXiv
  16. Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems, Mathematische Zeitschrif, (2018) 290:63-81, (with Ai-Hua Fan and Meng Wu) arXiv
  17. Dirichlet uniformly well-approximated numbers, International Mathematics Research Notices, to appear, (with Dong Han Kim) arXiv
  18. Metrical results on the distribution of fractional parts of powers of real numbers, Proceedings of Edinburgh Mathematical Society, 62 (2019), 505-521, (with Michał Rams and Yann Bugeaud) arXiv
  19. Hausdorff dimension of weighted singular vectors in R^2, Journal of the European Mathematical Society, to appear, (with Ronggang Shi, Omri Solan and Nattalie Tamam) arXiv

Syst¨¨mes dynamiques p-adiques, mesures de Gibbs p-adiques :

  1. p-adic repellers in Qp are subshifts of finite type, C. R. Acad. Sci. Paris, Ser. I 344 (2007) 219-224, (with Ai-Hua Fan, Yue-Fei Wang and Dan Zhou)
  2. On minimal decomposition of p-adic polynomial dynamical systems, Advances in Mathematics, 228, no. 4, (2011), 2116-2144, (with Ai-Hua Fan) arXiv
  3. On minimal decomposition of p-adic homographic dynamical systems, Advances in Mathematics, 257 (2014), 92-135, (with Ai-Hua Fan, Shi-Lei Fan and Yue-Fei Wang) arXiv
  4. Dynamics of convergent power series on the integral ring of a finite extension of Q_p, Journal of Differential Equations, 259 (2015)1628-1648, (with Shi-Lei Fan) arXiv
  5. Dynamics of the square mapping on the ring of p-adic integers, Proc. Amer. Math. Soc., 144 (2016), 1183-1196, (with Shi-Lei Fan) arXiv
  6. Dynamical structures of Chebyshev polynomials on Z_2, Journal of Number Theory, 169 (2016), 174-182, (with Shi-Lei Fan) arXiv
  7. Minimality of p-adic rational maps with good reduction, Discrete and Continuous Dynamical Systems -A, 37 (2017), 3161-3182, (with Ai-Hua Fan, Shi-Lei Fan and Yue-Fei Wang) arXiv
  8. Rational map ax+1/x on the projective line over Q_p, Contemporary Mathematics: Proccedings of 14th International Conference on P-adic Functional Analysis, 704(2018), 217-230, (with Shi-Lei Fan) arXiv
  9. Rational map ax+1/x on the projective line over Q_2, Sci China Math, 2018, 61: 2221-2236, (with Shi-Lei Fan) arXiv
  10. Periodic p-adic Gibbs measures of q-states Potts model on Cayley tree: The chaos implies the vastness of p-adic Gibbs measures, Journal of Statistical Physics, 171(2018),1000-1034, (with Mohd Ali Khameini Ahmad and Mansoor Saburov) arXiv

Autres syst¨¨mes dynamiques :

  1. Dynamical properties of negative beta transformation, Ergodic Theory and Dynamical Systems, 32, no. 5, (2012), 1673-1690, (with Wolfgang Steiner) arXiv
  2. On the shortest distance between orbits and the longest common substring problem, Advances in Mathematics, 344, (2019), 311-339, (with Vanessa Barros, J¨¦rôme Rousseau) arXiv

Articles soumis et prepublications

Articles en pr¨¦paration

Slides

S¨¦jours de Recheche

Liste de visites plus que 7 jours

Encadrement de Th¨¨se

  1. Ruxi SHI, Etude sur la conjecture de Fuglede et les suites oscillantes,
    ancien  ¨¦l¨¨ve normalien (Ulm), Contrat doctoral du Minist¨¨re de l'Education Nationale
    en cotutelle avec Ai-Hua FAN (Universit¨¦ de Picardie Jules Verne),
    soutenue le 26/06/2018, postdoc ¨¤ Universit¨¦ d'Oulu.
  2. Ali AHMAD, Mesures de Gibbs p-adiques sur les arbres de Cayley et syst¨¨mes dynamiques sur le corps des nombres p-adiques,
    Bourse de l'Ambassade de France en Malaisie et bourse Labex B¨¦zout, s¨¦jours en France du 01/10/2016 au 31/03/2018
    en cotutelle avec Mansoor SABUROV et Chin Hee PAH (Universit ́e Islamique Internationale de Malaisie)
    en cotutelle avec Arnaud LE NY (Universit¨¦ Paris-Est Cr¨¦teil),
    depuis septembre 2016.
  3. Lixuan ZHENG, B¨ºta-d¨¦veloppements et ses propri¨¦t¨¦s fractales,
    Bourse du China Scholarship Council, s¨¦jours en France du 29/09/2017 au 28/09/2019
    en cotutelle avec Min WU (Universit¨¦ de technologie de Chine m¨¦ridionale, Chine),
    depuis septembre 2017.
  4. Wanlou WU, Dimension de Hausdorff dans des syst¨¨mes dynamiques non-uniform¨¦ment hyperboliques,
    Bourse du China Scholarship Council, s¨¦jours en France du 08/10/2017 au 07/10/2019
    en cotutelle avec Dawei YANG (Universit¨¦ de Soochow, Chine),
    depuis octobre 2017.
  5. Kunkun SONG, Analyse multifractale et d¨¦composition minimale des syst¨¨mes dynamiques,
    Bourse du China Scholarship Council, s¨¦jours en France du 27/09/2018 au 26/09/2020
    en cotutelle avec Jihua MA (Universit¨¦ de Wuhan, Chine),
    depuis septembre 2018.

Collaborateurs

Mohd Ali Khameini AHMAD, Vanessa BARROS, Yann BUGEAUD, Ai-Hua FAN, Shi-Lei FAN, Thomas JORDAN, Dong Han KIM, Ji-Hua MA, Jacques PEYRIERE, Michał RAMS, J¨¦rôme ROUSSEAU, Mansoor SABUROV, St¨¦phane SEURET, Ronggang SHI, Ruxi SHI, Wolfgang STEINER, Omri SOLAN, Nattalie TAMAM, Bao-Wei WANG, Yue-Fei WANG, Meng WU, Jun WU, Dan ZHOU

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Last updated: December, 2018