Publications
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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.
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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.
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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.
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Skew products over translations on Td, d &ge 2.
B. Fayad
Proc. Amer. Math. Soc. volume
130 (2002), no. 1, p. 103--109.
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Partially mixing and locally rank 1 smooth transformations and flows on the torus.
B. Fayad
J. London Math. Soc.
64 (2001), p. 637-654.
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Weak mixing for reparameterized linear flows on the torus.
B. Fayad
Ergodic Theory Dynam. Systems, volume
22 (2002), no. 1, p. 187--201.
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Analytic mixing reparametrizations of irrational flows.
B. Fayad
Ergodic Theory Dynam. Systems
, volume
22 (2002), no. 2, p. 437--468.
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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.
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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.
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Constructions in elliptic dynamics.
B. Fayad, A. Katok
Dedicated to the memory of M. Herman,
Ergodic Theory Dynam. Systems, 24 (2004), p. 1477--1520.
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Weak mixing disc and annulus diffeomorphisms with
arbitrary Liouvillean rotation number on the boundary.
B. Fayad, Maria Saprykina
Ann. Sci. Ãcole Norm. Sup.
38 (2005), no. 3, p. 339--364.
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Rank one and mixing differentiable flows.
B. Fayad
Invent. Math.
160 (2005), no. 2, p. 305--340.
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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.
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A remark on conservative dynamics.
Jairo Bochi, B. Fayad, Enrique Pujals
Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), p. 763--766.
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On the ergodicity of the Weyl sums cocycle.
B. Fayad
Acta Arith. 125 (2006), p. 305--316.
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On the ergodicity of cylindrical transformations given by the
logarithm.
B. Fayad, Mariusz Lemanczyck
Moscow Math. J. 6 (2006), Number 4, p. 657--672.
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Mixing in the absence of the Shrinking Target Property.
B. Fayad
J. London Math. Soc. volume
38 (2006), p. 829--838.
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Smooth mixing flows with singular spectra.
B. Fayad
Duke Math. J. 132 Number 2 (2006), p. 371--391.
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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.
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Nonstandard Smooth Realizations of Liouville Rotations.
B. Fayad, M. Saprykina, A. Windsor
Ergodic Theory Dynam. Systems 27 (2007), p. 1803--1818.
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Exponential growth of products of matrices in SL(2,R).
B. Fayad, R. Krikorian
Nonlinearity 21 (2008), p. 319--323.
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Continuous spectrum on laminations over Aubry-Mather sets.
B. Fayad
Disc. and Cont. Dyn. Sys. 21 (2008), p. 823--834.
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Unbounded orbits for Semicircular Outer Billiard.
D. Dolgopyat, B. Fayad
Ann. Henri Poincare 10 (2008), p. 357--375.
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Rigidity results for SL(2,R)-cocycles.
B. Fayad, R. Krikorian
Journal of Modern Dynamics 3 (2009), p. 479--510.
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Smooth Linearization of commuting circle diffeomorphisms.
B. Fayad, K. Khanin
Ann. Math. 170 (2009),p. 961--980.
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Herman's last geometric theorem.
B. Fayad, R. Krikorian
Ann. Sci. Ecole Norm. Sup. 42 (2009), p. 193--219.
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A KAM scheme for SL(2,R)-cocycles with Liouvillean frequencies.
A. Avila, B. Fayad, R. Krikorian
GAFA 21-5 (2011), p. 1001--1019.
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KAM-tori near an analytic elliptic fixed point.
Hakan Eliasson, B. Fayad, R. Krikorian
Regular and Chaotic Dynamics, 18 (2013) p. 801--831.
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Deviations of Ergodic sums for Toral Translations I: Convex bodies.
D. Dolgopyat, B. Fayad
GAFA 24 (2014), p. 85--115.
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Analytic uniquely ergodic volume preserving maps on odd spheres.
B. Fayad, A. Katok
Commentarii Mathematici Helvetici 89 (2014), no.
4, p. 963-977.
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On manifolds supporting distributionally uniquely ergodic diffeomorphism.
A. Avila, B. Fayad, Alejandro Kocsard
Geometric and Functional Analysis 24, (2014)
p. 85-115.
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On the convergence to 0 of m_n x [1].
B. Fayad, Jean-Paul Thouvenot
Acta Arithmetica 165 (2014), no. 4, P. 327-332.
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Limit Theorems for toral translations
D. Dolgopyat, B. Fayad
Proceedings of Symposia in Pure Mathematics
Volume 89, 2015.
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Around the stability of KAM-tori.
Hakan Eliasson, B. Fayad, R. Krikorian
Duke Mathematical Journal 164
(2015), no. 9, 1733-1775.
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Multiple mixing for a class of conservative surface flows.
B. Fayad, A. Kanigowski
Inventions Mathematicae 203, (2016), p. 555--614
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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.
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On local rigidity of partially hyperbolic affine Zk actions.
D. Damjanovic, B. F.,
J. Reine Angew. Math. 2019
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Isolated elliptic fixed points for smooth Hamiltonians.
B. F., M. Saprykina,
Contemp. Math., 692, Amer. Math. Soc. 2017
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Double exponential stability of quasi-periodic motion in Hamiltonian systems.
A. Bounemoura, L. Niedermann, B. F.,
CMP 2017.
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Central limit theorems for simultaneous Diophantine approximations.
D. Dolgopyat, I. Vinogradov, B. F.,
Journal de l'Ecole Polytechnique 2017
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Singular spectrum for mixing Schrodinger operators
Y. Qu, B. F.,
Ergodic Theory and Dynamical Systems 2017
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An effective version of Katok's horseshoe theorem for conservative C2 surface diffeomorphisms.
Z. Zhang, B. F.,
Journal of Modern Dynamics 2017
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Attracted by an elliptic fixed point
J.-P. Marco, D. Sauzin, B. F.,
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Deviations of Ergodic sums for Toral Translations II: Boxes.
D. Dolgopyat, B. Fayad
PIHES 2020, p. 293-352
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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
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Super-exponential stability for generic real-analytic elliptic equilibrium points.
A. Bounemoura, B. Fayad, L. Niedermann
Adv. Math. 366 (2020), 30 pp
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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.
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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
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KAM tori are no more than sticky
D. Sauzin, B. F.,
Arch. Ration. Mech. Anal. 237 (2020), no. 3, 1177-1211.
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Non-differentiable irrational curves
for differentiable twist map
A. Avila, B. F.,
ETDS 2021
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Intertemporal Price Discrimination with Time-Varying Valuations
V. Araman, B. F.,
Operations Research 2020
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Instabilities of quasi-periodic tori
G. Farré, B. F.,
JEMS 2021
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Multiple Borel Cantelli Lemma in dynamics and MultiLog law for recurrence.
D. Dolgopyat, B. F., M. Saprykina
JMD 2021
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Topological weak mixing and diffusion at all times for a class of Hamiltonian systems
B. F., M. Saprykina
ETDS 2021
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Topological weak mixing and diffusion at all times for a class of Hamiltonian systems
B. F., M. Saprykina
ETDS 2021
Submitted for publication
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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
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Some questions around quasi-periodic dynamics
R. Krikorian, B. F.
Proceedings of the International Congress of Mathematicians 2018.