• Mechanisms for chaos pdf
  August, 2019 preprint (28 pages). (Notes for a lecture at VIASM )
  

• Symplectomorphisms with positive metric entropy (with A. Avila and S. Crovisier). pdf
  Proc. Lond. Math. Soc. 124 (2022), 691--712.

• Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms (with Danijela Damjanovic and Disheng Xu). pdf
  Duke Math J. 170 (2021), 3815--3890.

• Rigidity of some abelian-by-cyclic solvable group actions on T^N. (with Jinxin Xue). pdf
  Commun. Math. Phys. 376 (2020), 1223--1259.

• C^1 density of stable ergodicity (with A. Avila and S. Crovisier ). pdf
  Adv. Math. 379 (2021), 68 pp.
  

• Projective cocycles over SL(2, R) actions: measures invariant under the upper triangular group. (with Ch. Bonatti and Alex Eskin ). pdf
  Asterisque (2020), no. 415, 157--180.

• Diffeomorphisms with positive metric entropy (with A. Avila and S. Crovisier ). pdf
  Publ. Math. IHES. 124 (2016), 589--602.
  

• What is ... a blender? (with Ch. Bonatti, S. Crovisier and L. Diaz ). pdf
  Notices of the AMS 63 (2016), 1175--1178.
  

• Rates of mixing for the Weil-Petersson geodesic flow: Exponential mixing in exceptional moduli spaces.
  (with K. Burns, C. Matheus and H. Masur ). pdf
  Geom. Funct. Anal. (GAFA) 27 (2017) 240--288.
  

• Calculating the ★ connection.
  (with K. Burns, C. Matheus and H. Masur ). pdf
  May, 2016 preprint (14 pages).
  This paper is a supplement to our paper "Rates of mixing for the Weil-Petersson geodesic flow: Exponential mixing in exceptional moduli spaces": it contains the calculations justifying the statements of Lemma 4.8 and Proposition 4.10.
  

• What are Lyapunov exponents, and why are they interesting? pdf
  Bulletin of the AMS 54 (2017), 79--105.
  This article is based on notes for a lecture I gave for the Current Events Bulletin at the Joint Meetings in Seattle, January 2016.
  

• Rates of mixing for the Weil-Petersson geodesic flow I: No rapid mixing in non-exceptional moduli spaces.
  (with K. Burns, C. Matheus and H. Masur ). pdf
  Adv. Math. 306 (2017) 589--602.
  

• Lectures on marked length spectrum rigidity pdf
  Geometric group theory, IAS/Park City Math. Ser., 21 , (2014) 283--324.
  

• Cocycles over partially hyperbolic maps pdf
  (with A. Avila, J. Santamaria and M. Viana).
  
  This is the introduction to a volume of two long papers:
  The cohomological equation for partially hyperbolic diffeomorphisms and
  Holonomy invariance: rough regularity and applications to Lyapunov exponents (By A. Avila, J. Santamaria and M. Viana),
  both contained in a single volume: Asterisque , 358 (2013).
  

• Holder foliations, revisited pdf
  (with C. Pugh and M. Shub). Journal of Modern Dynamics , 6 (2012) 835--908.
  

• Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows pdf
  (with A. Avila and M. Viana). Journal of European Math Soc, 17 (2015) 1435--1462.
  

• The Weil-Petersson geodesic flow is ergodic pdf
  (with K. Burns and H. Masur ). Annals of Math , 175 (2012) 835--908.
  

• Conservative partially hyperbolic dynamics dvi or ps or pdf
  Proceedings of the International Congress of Mathematicians. Volume III, 1816--1836 (2010).
  

• Nonuniform center bunching and the genericity of ergodicity among
  C^1 partially hyperbolic symplectomorphisms dvi or ps or pdf
  (with A. Avila and J. Bochi) Ann. Sci. de l'Ecole Norm. Sup., 42 (2009) 931--979.
  

• The cohomological equation for partially hyperbolic diffeomorphisms pdf
  Asterisque , 358 (2013) 75--165.
  

• The C^1-generic diffeomorphism has trivial centralizer dvi or ps or pdf
  (with C. Bonatti and S. Crovisier) Publ. Math. IHES, 109 (2009) 185--244.
  

• Smooth ergodic theory (expository article for Encyclopedia of Complexity and System Science , 24 pages.) dvi or ps or pdf
  

• C^1-generic conservative diffeomorphisms have trivial centralizer dvi or ps or pdf
  (with C. Bonatti and S. Crovisier) Journal of Modern Dynamics 2 (2008), 359--373.
  

• Local density of diffeomorphisms with large centralizers dvi or ps or pdf
  (with C. Bonatti, S. Crovisier, and G. Vago) Ann. Sci. de l'Ecole Norm. Sup., 41 (2008) 925--954.
  

• Dynamical coherence and center bunching dvi or ps or pdf
  (with K. Burns) Discrete and Continuous Dynamical Systems, (Pesin birthday issue) 22 (2008), 89--100.
  

• The centralizer of a C^1 generic diffeomorphism is trivial (research announcement) dvi or ps or pdf
  (with C. Bonatti and S. Crovisier) Electronic Research Announcements in Mathematical Sciences 15 (2008), 33--43.
  

• On the ergodicity of partially hyperbolic systems dvi or ps or pdf
  (with K. Burns) Annals of Math 171 (2010) 451--489.
  

• Global rigidity of solvable group actions on S^1 (Revised May, 2004). dvi or ps or pdf
  (with L. Burslem ) Geometry and Topology 8 (2004), 877--924.
  

• Transitive partially hyperbolic diffeomorphisms on 3-manifolds (Revised October, 2004). dvi or ps or pdf
  (with C. Bonatti) Topology 44 (2005), no. 3, 475--508.
  

• Abundance of stable ergodicity (Revised May, 2004) dvi or ps or pdf
  (with C. Bonatti , C. Matheus and M. Viana). Comment. Math. Helv., 79 no. 9 (2004) 753-757.
  

• Random versus deterministic exponents in a rich family of diffeomorphisms. dvi or ps or pdf or gzipped ps
  (with F. Ledrappier, C. Simo and M. Shub). J. Stat. Phys. , 113 (2003), 85--149.
  Note that this is a large file. Only the .ps version has illustrations
  

• Partial differentiability of invariant splittings dvi or ps or pdf
  (with C. Pugh and M. Shub). J. Stat. Phys., 144 (2004) 891--921.
  

• Stable accessibility is C^1-dense. dvi or ps or pdf
  (with D. Dolgopyat) Asterisque , 287 (2003), 33--60.
  

• Recent results about stable ergodicity ps
  (with K. Burns, C. Pugh , and M. Shub). Proc. Symposia A.M.S., 69 (2001) 327-366.
  

• Absolutely singular dynamical foliations dvi or ps or pdf
  (with D. Ruelle). Comm. Math. Phys., 219 (2001) 481--487
  

• Pathological foliations and removable zero exponents dvi or ps or pdf
  (with M. Shub). Inventiones Math. 139 (2000), pp. 495-508.
  

• Stable ergodicity of skew products. dvi or ps or pdf
  (with K. Burns). Ann. Sci. de l'Ecole Norm. Sup., 32 (1999), pp. 859-889.
  

• Holder regularity of horocycle foliations. dvi or ps or pdf
  (with M. Gerber). J. Diff. Geom. 52 (1999) 41-72.
  

• Stably ergodic approximations: two examples. dvi or ps or pdf
  (with M. Shub). Erg. Th. Dyn. Syst. 20 (2000), no. 3, 875--893.
  

• Stable ergodicity and Anosov flows. dvi or ps or pdf
  (with K. Burns and C. Pugh ). Topology 39 (2000), pp. 149-159.
  

• Prevalence of non-Lipschitz Anosov foliations. dvi or ps or pdf
  (with B. Hasselblatt). Erg. Th. Dyn. Syst. 19 (1999), no. 3, pp. 643-656.
  

• Prevalence of non-Lipschitz Anosov foliations. (Research announcement) dvi or ps or pdf
  (with B. Hasselblatt). ERA Amer. Math. Soc. 3 (1997), pp. 93-98.
  

• Holder foliations.
  (with C. Pugh and M. Shub). Duke Math. J. 86, No.3 (1997), pp.517-546.
  Original paper pdf. Erratum dvi or ps or pdf
  

• Stable ergodicity of the time-one map of a geodesic flow.dvi or ps or pdf
  Thesis, University of California, Berkeley, May 1995. Erg. Th. Dyn. Syst. 18 No. 6 (1998) 1545-1588
  

• When an infinitely-renormalizable endomorphism of the interval can be smoothed. dvi or ps or pdf
  (with C. Tresser ). Fractals 3, No.4 (1995), pp.701-711.
  

• Circuits in Cayley digraphs of finite abelian groups.
  J. Graph Theory 14, No.1 (1990), pp.111-116.
  

Permanent preprints

• Diffeomorphisms with positive metric entropy (obsolete version) (with A. Avila and S. Crovisier ). pdf
  October, 2015 preprint (76 pages).
  Note: This paper has been split into two papers: Diffeomorphisms with positive metric entropy, and C1 -density of stable ergodicity (in preparation).
  

• A note on stable holonomy between centers. (preliminary version.) dvi or ps or pdf
  (with K. Burns) June, 2005 preprint. (11 pages).
  Note: This paper contains errors that have been rectified in a paper by Aaron Brown, which also contains more general results.
  

• C^1 genericity of trivial centralizers dvi or ps or pdf
  (with C. Bonatti and S. Crovisier) September, 2006 preprint. (47 pages).
  

• Better center bunching dvi or ps or pdf
  (with K. Burns) February, 2005 preprint. (35 pages).
  

• A stably Bernoullian diffeomorphism that is not Anosov dvi or ps or pdf
  (with M. Shub). 1998 IHES Preprint.