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.
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.
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.
Skew products over translations on Td, d &ge 2.
B. Fayad
Proc. Amer. Math. Soc. volume 130 (2002), no. 1, p. 103–109.
Partially mixing and locally rank 1 smooth transformations and flows on the torus.
B. Fayad
J. London Math. Soc. 64 (2001), p. 637-654.
Weak mixing for reparameterized linear flows on the torus.
B. Fayad
Ergodic Theory Dynam. Systems, volume 22 (2002), no. 1, p. 187–201.
Analytic mixing reparametrizations of irrational flows.
B. Fayad
Ergodic Theory Dynam. Systems , volume 22 (2002), no. 2, p. 437–468.
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.
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.
Constructions in elliptic dynamics.
B. Fayad, A. Katok
Dedicated to the memory of M. Herman, Ergodic Theory Dynam. Systems, 24 (2004), p. 1477–1520.
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.
Rank one and mixing differentiable flows.
B. Fayad
Invent. Math. 160 (2005), no. 2, p. 305–340.
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.
A remark on conservative dynamics.
Jairo Bochi, B. Fayad, Enrique Pujals
Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), p. 763–766.
On the ergodicity of the Weyl sums cocycle.
B. Fayad
Acta Arith. 125 (2006), p. 305–316.
On the ergodicity of cylindrical transformations given by the logarithm.
B. Fayad, Mariusz Lemanczyck
Moscow Math. J. 6 (2006), Number 4, p. 657–672.
Mixing in the absence of the Shrinking Target Property.
B. Fayad
J. London Math. Soc. volume 38 (2006), p. 829–838.
Smooth mixing flows with singular spectra.
B. Fayad
Duke Math. J. 132 Number 2 (2006), p. 371–391.
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.
Nonstandard Smooth Realizations of Liouville Rotations.
B. Fayad, M. Saprykina, A. Windsor
Ergodic Theory Dynam. Systems 27 (2007), p. 1803–1818.
Exponential growth of products of matrices in SL(2,R).
B. Fayad, R. Krikorian
Nonlinearity 21 (2008), p. 319–323.
Continuous spectrum on laminations over Aubry-Mather sets.
B. Fayad
Disc. and Cont. Dyn. Sys. 21 (2008), p. 823–834.
Unbounded orbits for Semicircular Outer Billiard.
D. Dolgopyat, B. Fayad
Ann. Henri Poincare 10 (2008), p. 357–375.
Rigidity results for SL(2,R)-cocycles.
B. Fayad, R. Krikorian
Journal of Modern Dynamics 3 (2009), p. 479–510.
Smooth Linearization of commuting circle diffeomorphisms.
B. Fayad, K. Khanin
Ann. Math. 170 (2009),p. 961–980.
Herman’s last geometric theorem.
B. Fayad, R. Krikorian
Ann. Sci. Ecole Norm. Sup. 42 (2009), p. 193–219.
A KAM scheme for SL(2,R)-cocycles with Liouvillean frequencies.
A. Avila, B. Fayad, R. Krikorian
GAFA 21-5 (2011), p. 1001–1019.
KAM-tori near an analytic elliptic fixed point.
Hakan Eliasson, B. Fayad, R. Krikorian
Regular and Chaotic Dynamics, 18 (2013) p. 801–831.
Deviations of Ergodic sums for Toral Translations I: Convex bodies.
D. Dolgopyat, B. Fayad
GAFA 24 (2014), p. 85–115.
Analytic uniquely ergodic volume preserving maps on odd spheres.
B. Fayad, A. Katok
Commentarii Mathematici Helvetici 89 (2014), no. 4, p. 963-977.
On manifolds supporting distributionally uniquely ergodic diffeomorphism.
A. Avila, B. Fayad, Alejandro Kocsard
Geometric and Functional Analysis 24, (2014) p. 85-115.
On the convergence to 0 of m_n x [1].
B. Fayad, Jean-Paul Thouvenot
Acta Arithmetica 165 (2014), no. 4, P. 327-332.
Limit Theorems for toral translations
D. Dolgopyat, B. Fayad
Proceedings of Symposia in Pure Mathematics Volume 89, 2015.
Around the stability of KAM-tori.
Hakan Eliasson, B. Fayad, R. Krikorian
Duke Mathematical Journal 164 (2015), no. 9, 1733-1775.
Multiple mixing for a class of conservative surface flows.
B. Fayad, A. Kanigowski
Inventions Mathematicae 203, (2016), p. 555–614
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.
On local rigidity of partially hyperbolic affine Zk actions.
D. Damjanovic, B. F.,
J. Reine Angew. Math. 2019
Isolated elliptic fixed points for smooth Hamiltonians.
B. F., M. Saprykina,
Contemp. Math., 692, Amer. Math. Soc. 2017
Double exponential stability of quasi-periodic motion in Hamiltonian systems.
A. Bounemoura, L. Niedermann, B. F.,
CMP 2017.
Central limit theorems for simultaneous Diophantine approximations.
D. Dolgopyat, I. Vinogradov, B. F.,
Journal de l’Ecole Polytechnique 2017
Singular spectrum for mixing Schrodinger operators
Y. Qu, B. F.,
Ergodic Theory and Dynamical Systems 2017
An effective version of Katok’s horseshoe theorem for conservative C2 surface diffeomorphisms.
Z. Zhang, B. F.,
Journal of Modern Dynamics 2017
Attracted by an elliptic fixed point
J.-P. Marco, D. Sauzin, B. F.,
Deviations of Ergodic sums for Toral Translations II: Boxes.
D. Dolgopyat, B. Fayad
PIHES 2020, p. 293-352
Zero entropy area preserving analytic diffeomorphisms of the disc are never mixing.
A. Avila, B. Fayad, P. Le Calvez, D. Xu, Z. Zhan
Invent. Math. 220 (2020), no. 3, 673-714
Super-exponential stability for generic real-analytic elliptic equilibrium points.
A. Bounemoura, B. Fayad, L. Niedermann
Adv. Math. 366 (2020), 30 pp
Erratic behavior for 1-dimensional random walks in a Liouville quasi-periodic environment
D. Dolgopyat, B. F., M. Saprykina
Electron. J. Probab. 26 (2021), Paper No. 66, 36 pp.
Lebesgue spectrum for area preserving flows on the two torus
G. Forni, A. Kanigowski, B. F.,
J. Amer. Math. Soc. 2021, doi.org/10.1090/jams/970
KAM tori are no more than sticky
D. Sauzin, B. F.,
Arch. Ration. Mech. Anal. 237 (2020), no. 3, 1177-1211.
Non-differentiable irrational curves for differentiable twist map
A. Avila, B. F.,
ETDS 2021
Intertemporal Price Discrimination with Time-Varying Valuations
V. Araman, B. F.,
Operations Research 2020
Instabilities of quasi-periodic tori
G. Farré, B. F.,
JEMS 2021
Multiple Borel Cantelli Lemma in dynamics and MultiLog law for recurrence.
D. Dolgopyat, B. F., M. Saprykina
JMD 2021
Topological weak mixing and diffusion at all times for a class of Hamiltonian systems
B. F., M. Saprykina
ETDS 2021
Topological weak mixing and diffusion at all times for a class of Hamiltonian systems
B. F., M. Saprykina
ETDS 2021
Submitted for publication
Lyapunov unstable elliptic equilibria
arXiv:1712.03001
Expository
Quasi-periodic dynamics : Introduction to KAM theory and Liouville constructions.
Jean-Christophe Yoccoz and the theory of circle diffeomorphisms.
H. Eliasson, R. Krikorian, B. F.
La gazette des mathématiciens 2018
Some questions around quasi-periodic dynamics
R. Krikorian, B. F.
Proceedings of the International Congress of Mathematicians 2018.