Publications of Amie Wilkinson

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.

Book

Geometry, Dynamics, and Rigidity Click here for FINAL pdf version . To be published by Princeton University Press.

Photo by Jessica Wynne.

Note that this is the form of the text that has been sent to typesetting. This means that the published book will have the same content, the same labeling of theorems, exercises, etc. It will not have the same pagination, and there will be further design elements in the published form.

I highly recommend you check out the published book and consider buying the hard copy (it lists at $75 and will have full color illustrations, plus a sewn binding -- pretty good for 600+ pages)! Here is the publisher's website for the book . The expected publication date is August, 2026. Comments are corrections are welcome (I will not change this version any further, but I do plan to post corrections).

Other preprints and publications

Marked Poincaré rigidity near hyperbolic metrics and injectivity of the Lichnerowicz Laplacian in dimension 3 (with K. Butt, A. Erchenko, T. Humbert, and T. Lefeuvre.) pdf
Preprint, 10/14/2025.

Minimality of strong foliations of Anosov diffeomorphisms (version 1) (with A. Avila and S. Crovisier). pdf
There will be two versions of this paper. In this version, we establish a criterion for robust minimality for strong unstable foliations, which will be used in other work.

The symmetries of affine K-systems and a program for centralizer rigidity (with D. Damjanovic, C. Wu, and D. Xu). pdf draft form .

Transitive centralizer and fibered partially hyperbolic systems (with D. Damjanovic and D. Xu). pdf
Int. Math. Res. Not. IMRN 12 (2024) 9686--9704

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), 42 (2022), 437--490.

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.