Click after the title to see the paper (requires a dvi, ps
or pdf viewer). All papers listed are also available in hard copy
on request.

**NOTE:** Figures appear only in the ps and pdf files.

**Absolute continuity, Lyapunov exponents and rigidity II : systems with compact center leaves**pdf

(with A. Avila and M. Viana).

*Erg. Th. Dyn. Syst. (Katok memorial issue),*

**Symplectomorphisms with positive metric entropy**(with A. Avila and S. Crovisier). pdf

*April, 2020 preprint (revision of March, 2019 preprint) (21 pages).*

**Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms**(with Danijela Damjanovic and Disheng Xu). pdf

*Duke Math J.*

**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. to appear.*

**Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group.**(with Ch. Bonatti and Alex Eskin ). pdf

*Asterisque to appear.*

**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**dvi or ps or pdf

C^1 partially hyperbolic symplectomorphisms

(with A. Avila and J. Bochi)*Ann. Sci. de l'Ecole Norm. Sup.,*

**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.

**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).