My profile in arXiv. My profile in Google Scholar.

PREPRINTS (available in here):

- "Robust transitivity and domination for endomorphisms with critical points" with C. Lizana, E. Pujals and W. Ranter (2021) Submitted.

- "Accesibility and ergodicity of collapsed Anosov flows" with S. Fenley (2021) Submitted.

- "Partial hyperbolicity and pseudo Anosov dynamics" with S. Fenley (2021) Submitted.

- "Collapsed Anosov flows and self orbit equivalences" with T. Barthelme and S. Fenley (2020) Submitted.


- ''Partially hyperbolic dynamics and 3-manifold topology '' (2021) to appear in Notices of the AMS.

- ``Research announcement: Partially hyperbolic diffeomorphisms homotopic to identity in 3-manifolds'' with T. Barthelme, S. Fenley and S. Frankel. Matrix Book Series. 2018 MATRIX Annals. Eds. D.R. Wood, J. de Gier, C.E. Praeger, T. Tao. Springer International Publishing, 2020.

- "Robust dynamics, invariant structures and topological classification''  Proceedings of ICM 2018 Vol 2 2057-2080. VIDEO OF THE TALK.

- "Partial hyperbolicity and classification: a survey" with A. Hammerlindl  Ergodic Theory and Dynamical Systems. 38 (2) (2018) 401-443.

- Introduction to non-uniform and partial hyperbolicity, Lecture notes for a minicourse (joint with M. C. Arnaud) in CIMPA "Hamiltonian and Lagrangian Dynamics" (Salto, March 2015). Published in Publicaciones Matematicas del Uruguay 16 (2016)

- "On the work of Jorge Lewowicz on expansive homeomorphisms" Publicaciones Matematicas del Uruguay 14 (2014) 6-22.


- "A remark on uniform expansion" to appear in Revista UMA.

- ''Eigenvalue gaps for hyperbolic groups and semigroups'' with F. Kassel , to appear in Journal of Modern Dynamics

- ''Topology of leaves for minimal laminations by hyperbolic surfaces'' with S. Alvarez, J. Brum and M. Martínez and an appendix with M. Wolff to appear in Journal of Topology

- ''Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds'' with S. Fenley to appear in Advances in Mathematics

- "Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3. Part II: Branching foliations" with T. Barthelme, S. Fenley and S. Frankel to appear in Geometry and Topology. .

- "Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3. Part I: The dynamically coherent case" with T. Barthelme, S. Fenley and S. Frankel to appear in Annales Scientifiques de l'ENS .

- ''Minimality of the action on the universal circle of uniform foliations'' with S. Fenley Groups, Geometry and Dynamics 15 (2021), no. 4, 1489–1521.

- "Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms" with T. Barthelme, S. Fenley and S. Frankel Ergodic Theory and Dynamical Systems 41 (2021), no. 11, 3227-3243.

''Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence'' with C. Bonatti , A. Gogolev and A. Hammerlindl Geometry and Topology. 24:4, 1751--1790, (2020).

- ''Some remarks on projectively Anosov flows'' with C. Bonatti and J. Bowden, Matrix Book Series. 2018 MATRIX Annals. Eds. D.R. Wood, J. de Gier, C.E. Praeger, T. Tao. Springer International Publishing, 2020.

- ``Classification of systems with center stable tori'' with A. Hammerlindl . Michigan Mathematical Journal, 68 (2019), no. 1, 147–166.

- ``Finiteness of partially hyperbolic attractors with one dimensional center'' with S. Crovisier and M. Sambarino, Annales Scientifiques de l'ENS, 53 (2020) 559-588.

- ``Seifert manifolds admitting partially hyperbolic diffeomorphisms'' with A. Hammerlindl and M. Shannon,  Journal of Modern Dynamics. 12 (2018) 193-222.

"Rotation intervals and entropy on attracting annular continua" with A. Passeggi and M. Sambarino. Geometry and Topology.  22 (4) (2018)  2145-2186.

- "Anosov representations and dominated splittings" with J. Bochi and A. Sambarino Journal of the European Math. Soc. 21 (2019), no. 11, pp. 3343-3414.

- ``Free orbits for minimal actions on the circle'' with J. Brum and M. Martinez. Proceedings AMS. 146 (2) (2018) 581-587.

- "Many intermingled basins in dimension 3" with C. Bonatti , Israel Journal of Math. 224 (1) (2018) 293-314.

- "Eigenvalues and entropy of a Hitchin representation" with A. Sambarino  Inventiones Math. 209 Issue 3 (2017) 885-925.

- "Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples" with C. Bonatti and A. GogolevInventiones Math.  Vol.206 Iss. 3. (2016) pp.801-836.

- "Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples" with C.Bonatti and K.ParwaniAnnales Scientifiques de l'ENS. Vol. 49 Fas. 6 (2016).

- "Livsic theorem for low-dimensional diffeomorphism cocycles" with A. Kocsard. Comentarii Math. Helvetici. Vol 91 Issue 1 (2016) p.39-64.

- "Partially hyperbolic diffeomorphisms with a trapping propertyDiscrete and Continuous Dynamical Systems A  Vol. 35 Issue. 10 (2015).

"Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group" with A. Hammerlindl.   Journal of Topology. 8 (3) (2015) 

- "A few remarks on partially hyperbolic diffeomorphisms of T3 isotopic to Anosov Journal of Dynamics and Differential Equations 26 (3) (2014) pp 805-815..

- "Dynamical coherence for partially hyperbolic diffeomorphisms of tori isotopic to Anosov" with T. Fisher and M. SambarinoMathematische Zeitchcrift  278 (2014) pp 149-168

- "Pointwise partial hyperbolicity in three dimensional nilmanifolds" with A. Hammerlindl. Journal of the London Math. Society 89 n3 (2014) 853-875.

- "Partial hyperbolicity and foliations in T3" Journal of Modern Dynamics Vol. 9 Issue 1 (2015) 81-121.

- "Tame dynamics and robust transitivity: Chain recurrence classes versus homoclinic classes" with C. Bonatti, S. Crovisier and N. Gourmelon. Transactions of the AMS 366 n9 (2014) 4849-4871.

- "Wild Milnor attractors accumulated by lower dimensional dynamics" Ergodic Theory and Dynamical Systems 34 n1 (2014) 236-262.

- "Recurrence of non-resonant torus homeomorphisms" Proceedings of the AMS. 140 (2012) 3973-3981.

- "Generic bi-Lyapunov stable homoclinic classes" Nonlinearity 23 n7 (2010) 1631-1650.

- "Codimension one homoclinic classes with non-empty interior" with M. Sambarino, Bulletin of the Brazil Math. Soc.  41 n1 (2010) 125-138.

- "Local implications of almost global stability" with P. Monzon, Dynamical Systems: An International Journal. 24 n1 (2009) 109-115.

- "Local product structure for expansive homeomorphisms" with A. Artigue and J. Brum. Topology and its applications. 156 n4 (2009) 674-685.

- "Local and global aspects of almost global stability" with P. Monzon. Proceedings of the 45th IEEE Conference on Decicion and Control (2006).

COLLABORATORS: List of colleagues I am working, have worked with or have ongoing projects with. 

Flavio Abdenur

Sebastien Alvarez

Alfonso Artigue  

Thomas Barthelme

Jairo Bochi

Christian Bonatti

Jonathan Bowden

Joaquin Brum

Sylvain Crovisier

Alex Eskin

Sergio Fenley

Todd Fisher 

Steven Frankel 

Andrey Gogolev 

Nicolas Gourmelon 

Andy Hammerlindl

Fanny Kassel

Alejandro Kocsard

Cristina Lizana

Matilde Martinez

Pablo Monzon

Kamlesh Parwani

Alejandro Passeggi

Enrique Pujals

Wagner Ranter

Andrés Sambarino

Martín Sambarino

Mario Shannon

Maxime Wolff

Zhiyuan Zhang


Ian Agol  Alexander Arbieto     Marie Claude Arnaud     Artur Avila     Viviane Baladi    Thierry Barbot   Juliette Bavard   Yves Benoist   

Francois Beguin   Pierre Berger  Martin Bridgeman   Misha Brin Aaron Brown  Abed Bounemoura  Jonathan Bowden  Keith Burns  Clark Buttler

 Jerome Buzzi      Richard Canary  Eleonora Catsigeras  Danny Calegari Indira Chatterji Vaughan Climenhaga   Gonzalo Contreras    

Daniel Coronel  Francoise Dal'bo Jeffrey Danciger Bertrand Deroin  Lorenzo Diaz  Dimitry Dolgopyat   Romain Dujardin Alex Eskin    

Benson Farb  Bassam Fayad   Simion Filip  David Fisher  Alex Furman Shaobo Gan   Katrin Gelfert  Etienne Ghys Bill Goldman  Marcel Guardia 

Mikail Gromov  Olivier Guichard Boris Hasselblatt  Steve Hurder  Sebastian Hurtado  Sergei Ivanov   Tobias Jaeger    Boris Kalinin  

Vadim Kaloshin  Misha Kapovich  Fanny Kassel   Anatole Katok    Svetlana Katok  Bruce Kleiner  Andres Koropecki    Francois Labourie 

Pablo Lessa  Frederic Le Roux Misha Lyubich  Yuri Lima   Kathryn Mann  Vlad Markovic  Ludovic Marquis Marco Martens Carlos Matheus

Curt McMullen  John Milnor  Emmanuel Militon  Andres Navas  Maria Jose Pacifico Pierre Pansu Gabriel Paternain  Yakov Pesin   Mario Ponce  

Enrique Pujals   Jean-Francois Quint  Ludovic Rifford Juan Rivera-Letelier  Jana Rodriguez Hertz    Victoria Sadovskaya    Bruno Santiago  

Omri Sarig    Mike Shub   Ali Tahzibi  Philippe Thieullin  Nicolas Tholozan  Michele Triestino  Carlos Vasquez   Marcelo Viana  Raul Ures 

Anna Wienhard  Amie Wilkinson Dave Witte-Morris Maxime Wolff  Alex Wright   Jean-Cristophe Yoccoz  Lai-Sang Young



- "Partially hyperbolic diffeomorphisms homotopic to identity in dimension 3" with T. Barthelme, S. Fenley and S. Frankel (2019) This paper was split in two for submission. Announcement (2018).

- Anosov representations. Lecture notes for a minicourse in Beyond Uniform Hyperbolicity (Provo, UTAH, june 2017) joint with F. Kassel. 

- Introduction to partially hyperbolic dynamics, (with S. Crovisier). Lecture notes for a minicourse in School and Conference in Dynamical Systems (ICTP, Trieste, July 2015).

- Entropía y Topologia: Lecture notes for a minicourse (joint with M. Shub) in Montevideo, March-April 2014 (In spanish).

- Classification of partially hyperbolic diffeomorphisms in 3-dimensional manifolds. Lecture notes for a minicourse in "A week of dynamical systems at UFRJ" (Rio de Janeiro, January 2013)

- "Non existence of attractors and dynamics around some wild homoclinic classes" Preprint (Previous version of my paper "Wild homoclinic classes...")

- "A proof of the existence of attractors in dimension 2" Preprint (2009). Not intended for publication (The results can be cited from my thesis where there is a longer presentation of this result).




PHD Thesis: Partial hyperbolicity and attracting regions in 3-dimensional manifolds. Advisors: Sylvain Crovisier and Martin Sambarino. Defended: July 2012.

Master Thesis: Clases homoclinicas genericas con interior. Advisor: Martin Sambarino. Defended: August 2008.

Degree Monograph: Transitividad robusta en superficies. Advisor: Martin Sambarino. Defended: March 2007.




``Coarse dynamics and partially hyperbolic diffeomorphisms in 3-manifolds'' Members Seminar. Institute for Advanced Study (Princeton, NJ, February 2020.) VIDEO OF THE TALK.

``Some dynamics on hyperbolic 3-manifolds'' Plenary talk. 32 Coloquio Brasilero de Matemática (IMPA, Rio, August 2019) VIDEO OF THE TALK.

``Robust dynamics, invariant geometric structures and topological classification'' Dynamical Systems Session, International Congress of Mathematicians Rio 2018.  VIDEO OF THE TALK. Official version.

``Rigidité de régularité pour les représentations de Hitchin'' Seminaire Geometrie et Groupes Discretes  IHES (Bures-sur-Ivette) (April 2017)

``Partial hyperbolicity in 3-manifolds: abundance of mapping classes and non-integrability'' Geometry and Topology Seminar Yale University (April 2017)

``Partial hyperbolicty and foliations in 3-manifolds'' Cuernavaca's Friends 20 years (January 2017). VIDEO OF THE TALK.

"Partial hyperbolicity and foliations in 3-manifolds" IV EBSD Campinas (October 2016).

"Dynamics in the study of discrete subgroups of Lie groups" V CLAM, Barranquilla (July 2016).

"Entropy rigidity for surface group representations" International Conference on Dynamical Systems, Buzios (July 2016)

"Anosov representations and dominated splittings" Workshop on Geometry and Groups in Montevideo. (April 2016)

"The classification problem for partially hyperbolic diffeomorphisms" Third Palis Balzan Symposium on Dynamical Systems, IHP (Paris June 2015)

"Discrete subgroups of Lie Groups" (In spanish) Seminario de Sistemas Dinamicos de Montevideo (Uruguay,  April 2015).

"Partially hyperbolic examples in dimension 3" 3era Escola Brasileira de Sistemas Dinámicos, Bento Goncalves (Porto Alegre, October 2014)

"Rigidity of eigenvalues for Hitchin representations" (in spanish)  Seminario de Sistemas Dinamicos de Montevideo (Uruguay,  October 2014).

"Geometry of the strong foliations in partially hyperbolic attractors" International Conference in Dynamical Systems IMPA (Rio November 2013)

"Cocycles of diffeomorphisms over a hyperbolic basis" University of Chicago Dynamical Systems Seminar(November 2013)

"Global stability for partially hyperbolic diffeomorphisms isotopic to Anosov" Northwestern UniversityDynamical Systems Seminar (Evanston, November 2013)

"Partial hyperbolicity and foliations in certain 3-manifolds" SUNY Binghampton Geometry and Topology Seminar (October 2013)

"The geometry of partially hyperbolic attractors" 2nd Palis-Balzan Symposium (IHP, Paris June 2013)

Slides for the (joint with Andy Hammerlindl) minicourse "Classification of partially hyperbolic diffeomorphisms in certain 3-manifolds" in the conference Beyond Uniform Hyperbolicity (Bedlewo, Poland May 2013). See alsoAndy's page

Lecture 1, 2, 3, 4, 5, 6

"On the work of Jorge Lewowicz on expansive homeomorphisms" Montevideo Conference in Dynamical Systems (August 2012).

"Robust dynamical properties and geometric structures in
dimension 3"
 IV CLAM, Cordoba (August 2012).

"Partial hyperbolicity and attracting regions in 3-dimensional manifolds" PhD defense (July 2012)

"Partial hyperbolicity and leaf conjugacy in nilmanifolds" Palis-Balzan conference (June 2012)

 "Partial hyperbolicty and leaf conjugacy in small 3-manifolds" ICTP-Trieste (June 2012).

“Partially hyperbolic diffeomorphisms of T^3” Puc�n Chile Conferencia en honor a Rodrigo Bamon (Noviembre 2011).

 “Partial hyperbolicity and foliations” EDAI (Noviembre 2011)

Codimension one generic homoclinic clases with interior” Poster presented in the 1st seminaire MathAMSUD in Lima, Peru (November 2008).

"Local and global aspects of almost global stability"  For the 45th IEEE Conference on Decision and Control, San Diego (2006).