Publications

  1. Topologically mixing and minimal but not ergodic, analytic transformation on T5.
    B. Fayad
    Bol. Soc. Brasil. Mat. (N.S.) , volume 31 (2000), no. 3, p. 277--285.
  2. Mixed spectrum reparameterizations of linear flows on T2.
    B. Fayad, Anatole Katok, Alistair Windsor
    Dedicated to the memory of I. G. Petrovskii on the occasion of his 100th anniversary , Mosc. Math. J. volume 1 (2001), no. 4, p. 521--537.
  3. Polynomial decay of correlations for a class of smooth flows on the two torus.
    B. Fayad
    Bull. Soc. Math. France tome 129 (2001), no. 4, p. 487--503.
  4. Skew products over translations on Td, d &ge 2.
    B. Fayad
    Proc. Amer. Math. Soc. volume 130 (2002), no. 1, p. 103--109.
  5. Partially mixing and locally rank 1 smooth transformations and flows on the torus.
    B. Fayad
    J. London Math. Soc. 64 (2001), p. 637-654.
  6. Weak mixing for reparameterized linear flows on the torus.
    B. Fayad
    Ergodic Theory Dynam. Systems, volume 22 (2002), no. 1, p. 187--201.
  7. Analytic mixing reparametrizations of irrational flows.
    B. Fayad
    Ergodic Theory Dynam. Systems , volume 22 (2002), no. 2, p. 437--468.
  8. Topologically mixing flows with pure point spectrum.
    B. Fayad
    Proceedings of the research trimester on dynamical systems (Pisa 2002). Pubblicazioni della Classe di Scienze, Scuola Normale Superiore, Pisa.
  9. Non unmiform hyperbolicity and elliptic dynamics.
    B. Fayad
    in Modern Dynamical Systems and Applications, edited by M. Brin, B. Hasselblatt, Y. Pesin, (2004) Cambridge, p. 325--330.
  10. Constructions in elliptic dynamics.
    B. Fayad, A. Katok
    Dedicated to the memory of M. Herman, Ergodic Theory Dynam. Systems, 24 (2004), p. 1477--1520.
  11. Weak mixing disc and annulus diffeomorphisms with arbitrary Liouvillean rotation number on the boundary.
    B. Fayad, Maria Saprykina
    Ann. Sci. École Norm. Sup. 38 (2005), no. 3, p. 339--364.
  12. Rank one and mixing differentiable flows.
    B. Fayad
    Invent. Math. 160 (2005), no. 2, p. 305--340.
  13. A dichotomy between uniform hyperbolicity and zero Lyapunov epxonents for SL(2,R) cocycles
    Jairo Bochi, B. Fayad
    Bull. of the Braz. Math. Soc., 37, no. 3 (2006), p. 307--349.
  14. A remark on conservative dynamics.
    Jairo Bochi, B. Fayad, Enrique Pujals
    Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), p. 763--766.
  15. On the ergodicity of the Weyl sums cocycle.
    B. Fayad
    Acta Arith. 125 (2006), p. 305--316.
  16. On the ergodicity of cylindrical transformations given by the logarithm.
    B. Fayad, Mariusz Lemanczyck
    Moscow Math. J. 6 (2006), Number 4, p. 657--672.
  17. Mixing in the absence of the Shrinking Target Property.
    B. Fayad
    J. London Math. Soc. volume 38 (2006), p. 829--838.
  18. Smooth mixing flows with singular spectra.
    B. Fayad
    Duke Math. J. 132 Number 2 (2006), p. 371--391.
  19. A Dichotomy between discrete and continuous spectrum for a class of special flows over rotations.
    B. Fayad, AListair Windsor
    J. Mod. Dyn. 1 (2007), no. 1, p. 107--122.
  20. Nonstandard Smooth Realizations of Liouville Rotations.
    B. Fayad, M. Saprykina, A. Windsor
    Ergodic Theory Dynam. Systems 27 (2007), p. 1803--1818.
  21. Exponential growth of products of matrices in SL(2,R).
    B. Fayad, R. Krikorian
    Nonlinearity 21 (2008), p. 319--323.
  22. Continuous spectrum on laminations over Aubry-Mather sets.
    B. Fayad
    Disc. and Cont. Dyn. Sys. 21 (2008), p. 823--834.
  23. Unbounded orbits for Semicircular Outer Billiard.
    D. Dolgopyat, B. Fayad
    Ann. Henri Poincare 10 (2008), p. 357--375.
  24. Rigidity results for SL(2,R)-cocycles.
    B. Fayad, R. Krikorian
    Journal of Modern Dynamics 3 (2009), p. 479--510.
  25. Smooth Linearization of commuting circle diffeomorphisms.
    B. Fayad, K. Khanin
    Ann. Math. 170 (2009),p. 961--980.
  26. Herman's last geometric theorem.
    B. Fayad, R. Krikorian
    Ann. Sci. Ecole Norm. Sup. 42 (2009), p. 193--219.
  27. A KAM scheme for SL(2,R)-cocycles with Liouvillean frequencies.
    A. Avila, B. Fayad, R. Krikorian
    GAFA 21-5 (2011), p. 1001--1019.
  28. KAM-tori near an analytic elliptic fixed point.
    Hakan Eliasson, B. Fayad, R. Krikorian
    Regular and Chaotic Dynamics, 18 (2013) p. 801--831.
  29. Deviations of Ergodic sums for Toral Translations I: Convex bodies.
    D. Dolgopyat, B. Fayad
    GAFA 24 (2014), p. 85--115.
  30. Analytic uniquely ergodic volume preserving maps on odd spheres.
    B. Fayad, A. Katok
    Commentarii Mathematici Helvetici 89 (2014), no. 4, p. 963-977.
  31. On manifolds supporting distributionally uniquely ergodic diffeomorphism.
    A. Avila, B. Fayad, Alejandro Kocsard
    Geometric and Functional Analysis 24, (2014) p. 85-115.
  32. On the convergence to 0 of m_n x [1].
    B. Fayad, Jean-Paul Thouvenot
    Acta Arithmetica 165 (2014), no. 4, P. 327-332.
  33. Limit Theorems for toral translations
    D. Dolgopyat, B. Fayad
    Proceedings of Symposia in Pure Mathematics Volume 89, 2015.
  34. Around the stability of KAM-tori.
    Hakan Eliasson, B. Fayad, R. Krikorian
    Duke Mathematical Journal 164 (2015), no. 9, 1733-1775.
  35. Multiple mixing for a class of conservative surface flows.
    B. Fayad, A. Kanigowski
    Inventions Mathematicae 203, (2016), p. 555--614
  36. Rigidity times for weakly mixing dynamical system which are not rigidity times for any irrational rotation.
    B. Fayad, Adam Kanigowski
    Ergodic Theory and Dynamical Systems, 35 (2015) p. 2529-2534.
  37. On local rigidity of partially hyperbolic affine Zk actions.
    D. Damjanovic, B. F., to appear in
    Journal fur die reine ind angewandte Mathematik.https://doi.org/10.1515/crelle-2016-0059
  38. KAM-instability of elliptic fixed points in arbitrary frequency.
    B. F., M. Saprykina, to appear in
    AMS Contemporary Mathematics, volume to the memory of Anosov. arXiv:1602.02659.
  39. Double exponential stability of quasi-periodic motion in Hamiltonian systems.
    A. Bounemoura, L. Niedermann, B. F.,
    to appear in CMP, arXiv:1601.01783.
  40. Central limit theorems for simultaneous Diophantine approximations.
    D. Dolgopyat, I. Vinogradov, B. F.,
    Journal de l'Ecole Polytechnique Vol. 4 (2017), p. 1-35.
  41. Singular spectrum for mixing Schrodinger operators
    Y. Qu, B. F.,
    Ergodic Theory and Dynamical Systems https://doi.org/10.1017/etds.2017.26.
  42. An effective version of Katok's horseshoe theorem for conservative C2 surface diffeomorphisms.
    Z. Zhang, B. F.,
    Journal of Modern Dynamics (2017), p. 425-445
  43. Attracted by an elliptic fixed point
    J.-P. Marco, D. Sauzin, B. F.,
    To appear in Asterisque, Special Volume dedicated to the memory of J.-C. Yoccoz
  44. Submitted for publication

  45. Deviations of Ergodic sums for Toral Translations II: Boxes.
    D. Dolgopyat, B. Fayad
    arXiv:1211.4323
  46. Zero entropy area preserving analytic diffeomorphisms of the disc are never mixing.
    A. Avila, B. Fayad, P. Le Calvez, D. Xu, Z. Zhan
    arXiv:1509.06906
  47. Double exponential stability for generic real-analytic elliptic equilibrium points.
    A. Bounemoura, B. Fayad, L. Niedermann
    arXiv:1509.00285
  48. Lebesgue spectrum for area preserving flows on the two torus
    G. Forni, A. Kanigowski, B. F.,
    arXiv:1609.03757
  49. Lyapunov unstable elliptic equilibria
    B. F.
  50. Some questions around quasi-periodic dynamics
    R. Krikorian, B. F.
  51. KAM tori are no more than sticky
    D. Sauzin, B. F.,
  52. Non-differentiable minimal curves for differentiable twist map
    A. Avila, B. F.,
  53. Expository

  54. Quasi-periodic dynamics : Introduction to KAM theory and Liouville constructions

  55. Jean-Christophe Yoccoz and the theory of circle diffeomorphisms.
    H. Eliasson, R. Krikorian, B. F.