Research Interests
Dynamical Systems and Ergodic Theory
Education
Ph.D. 1993 IMPA, Rio de Janeiro, Brazil
B. S. 1990 University of the Republic, Uruguay
Employment
2016- present Professor of Mathematics, Southern University of Science and Technology
2002- 2016 Professor of Mathematics, Univerisity of the Republic, Uruguay
1995-2002 Associate Professor, Univerisity of the Republic, Uruguay
1993-1995 Assistant Professor, Univerisity of the Republic, Uruguay
1987-1993 Teaching Assistant, Univerisity of the Republic, Uruguay
Honors
· Simons Associate, ICTP, Trieste, Italy, since 2014.
· Researcher of the PEDECIBA (program of basic sciences, Uruguay) since 1994 (at the highest level since 2013)
Selected Publications
· A non-dynamically coherent example on T3, Annales de l’Institut Henri Poincaré, Vol. 33, 1023-1032, 2016, joint with F. Rodriguez Hertz and J. Rodriguez Hertz.
· Intrinsic ergodicity of partially hyperbolic diffeomorphisms with hyperbolic linear part, Proceedings of the American Mathematical Society, Vol. 140, 1973–1985, 2012.
· New criteria for ergodicity and non-uniform hyperbolicity, Duke Mathematical Journal, Vol. 160, 599–629, 2011, joint with F. Rodriguez Hertz, J. Rodriguez Hertz and A. Tahzibi.
· Tori with hyperbolic dynamics in 3-manifolds, Journal of Modern Dynamics, Vol. 5, 185–202, 2011, joint with F. Rodriguez Hertz and J. Rodriguez Hertz.
· Uniqueness of SRB measures on surfaces, Communications in Mathematical Physics, Vol. 306, 35–49, 2011, joint with F. Rodriguez Hertz, J. Rodriguez Hertz and A. Tahzibi.
· Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d-centerbundle, Inventiones Mathematicae, Vol. 172, 353–381, 2008, joint with F. Rodriguez Hertz and J. Rodriguez Hertz.
· Partial hyperbolicity and ergodicity in dimension 3, Journal of Modern Dynamics, Vol. 2, 187–208, 2008, joint with F. Rodriguez Hertz and J. Rodriguez Hertz.
· A survey of partially hyperbolic dynamics, Fields Institute Comm. , Vol. 51, 35–88, 2007, joint with F. Rodriguez Hertz and J. RodriguezHertz.
· Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms, Journal de l’Institut de Mathématiques de Jussieu, Vol.1(4), 513–541, 2002, joint with C. Bonatti and L. J. Díaz.
· Partial hyperbolicity and robust transitivity, Acta Mathematica, Vol. 183, 1–43, 1999, joint with L.J. D´ıaz and E. Pujals.
· Abundance of hyperbolicity in the C1 topology, Annales Scientifiques de L’Ecole Normale Superieure, quatriéme série, t. 28, 747–760, 1995.
Academic papers
(1) Robust minimality of strong foliations for DA diffffeomorphisms: cu-volume expansion and new examples, joint with M. A. Rodriguez Hertz and J. Yang, Trans. Amer. Math. Soc. 375 (2022), no. 6, 4333–4367.
(2) Maximal entropy measures of diffffeomorphisms of circle fifiber bundles, joint with M. Viana and J. Yang, Journal of the London Math. Soc. 103 (2021), 1016-1034.
(3) Ergodicity and partial hyperbolicity on Seifert manifolds, joint with A. Hammerlindl and J. Rodriguez Hertz, Journal of Modern Dynamics 16 (2020), 331–348.
(4) On the three-legged accessibility property, joint with M. A. Rodriguez Hertz, New trends in One Dimensional Dynamics, Springer Proceedings in Mathematics & Statistics, vol 285, 239–248, 2019.
(5) Partially hyperbolic dynamics in dimension three, joint with P. Carrasco, F. Rodriguez Hertz and M. A. Rodriguez Hertz, Ergodic Theory and Dynamical Systems 38 8 (2018), 2801–2837.
(6) On the non-robustness of intermingled basins, joint with Carlos V´asquez, Ergodic Theory and Dynamical Systems, 38 1 (2018), 384–400.
(7) A non-dynamically coherent example in T3, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Annales de l‘Institut Henri Poincar´e. Analyse Non Linaire , 33, 4 (2016), 1023-1032.
(8) Center-unstable foliations do not have compact leaves, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Mathematical Research Letters, vol 23, 1819-1832, 2016.
(9) Ergodicity and partial hyperbolicity on the 3-torus, joint with A. Hammerlindl, Communications in Contemporary Mathematics, vol. 16, 1350038 (22 pages), 2014.
(10) Intrinsic ergodicity of partially hyperbolic diffffeomorphisms with hyperbolic linear part, Proceedings of the American Mathematical Society, vol. 140, 1973-1985, 2012.
(11) Maximizing measures for partially hyperbolic systems with compact center leaves, joint with F. Rodriguez Hertz, M. A. Rodriguez Hertz and A. Tahzibi, Ergodic Theory and Dynamical Systems, Vol 32, 825-839, 2012.
(12) New criteria for ergodicity and non-uniform hyperbolicity, joint with F. Rodriguez Hertz, M. A. Rodriguez Hertz and A. Tahzibi, Duke Mathematical Journal, Vol 160, 599-629, 2011.
(13) Tori with hyperbolic dynamics in 3-manifolds, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Journal of Modern Dynamics, vol. 5, 185-202, 2011.
(14) Uniqueness of SRB measures on surfaces, joint with F. Rodriguez Hertz, M. A. Rodriguez Hertz and A. Tahzibi, Communications in Mathematical Physics, vol. 306, n 1, 35-49, 2011.
(15) Accessibility and abundance of ergodicity in dimension three: a survey, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Publicaciones Matematicas del Uruguay, especial volume, Proceeding of the First Colloquium Franco-Uruguayan of Mathematics, vol. 12, 177-198, 2011.
(16) Creation of blenders in the conservative setting, joint with F. Rodriguez Hertz, M. A. Rodriguez Hertz and A. Tahzibi, Nonlinearity, vol. 23, 211-223 2010.
(17) Accessibility and stable ergodicity for partially hyperbolic diffffeomorphisms with 1d-center bundle, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Inventiones Mathematicae, vol. 172, 353-381 2008.
(18) Partial hyperbolicity and ergodicity in dimension 3, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Journal of Modern Dynamics, vol. 2, 187-208, 2008.
(19) Density of accessibility for partially hyperbolic diffffeomorphisms with one dimensional center, joint with K. Burns, F. Rodriguez Hertz, M. A. Rodriguez Hertz and A. Talitskaya, Discrete and Continuous Dynamical Systems, vol. 22, 75-88, 2008.
(20) On existence and uniqueness of weak foliations in dimension 3, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Contemporary Mathematics, vol. 469, 303-316, 2008.
(21) A criterion for ergodicity of non-uniformly hyperbolic diffffeomorphisms, joint with F. Rodriguez Hertz, M. A. Rodriguez Hertz and A. Tahzibi, ERA-MS, vol. 14, 74-81, 2007.
(22) Some results on the integrability of the center bundle for partially hyperbolic diffffeomorphisms, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Fields Institute Comm., vol. 51, 103-112, 2007.
(23) A survey of partially hyperbolic dynamics, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Fields Institute Comm., vol. 51, 35-88, 2007.
(24) On basic pieces of Axiom A diffffeomorphisms isotopic to pseudo-Anosov maps, joint with J. Lewowicz, Asterisque, Vol 287, 125-134, 2003.
(25) Critical saddle-node cycles: Hausdorffff dimension and persistence of tangencies, joint with L. J. D´ıaz, Ergodic Theory and Dynamical Systems, Vol 22, 1117-1140, 2002.
(26) Minimality of strong stable and unstable foliations for partially hyperbolic diffffeomorphisms, joint with C. Bonatti and L. J. D´ıaz, Journal de l’Institut de Math´ematiques de Jussieu, vol.1 (4), 513-541, 2002.
(27) On manifolds supporting Quasi-Anosov diffffeomorphisms, joint with M. A. Rodriguez Hertz and J.L. Vieitez, Comptes Rendus de l’Acad´emie des Sciencies de Paris, S´erie I 334, 321-323, 2002.
(28) On Smale diffffeomorphisms close to pseudo-Anosov maps, joint with J. Lewowicz, Journal of the Brazilian Society of Computational and Applied Mathematics (CAAM), Vol 20, 187-194, 2001.
(29) Partial hyperbolicity and robust transitivity, joint with L.J. D´ıaz and E. Pujals, Acta Mathematica, vol. 183, 1-43, 1999.
(30) H´enon attractors: SBR measures and Dirac measures for sinks, International Conference on Dynamical Systems, Montevideo, Pitman Research Notes in Math. Series (362), Editores: F. Ledrappier, J. Lewowicz & S. Newhouse, p. 214-220, 1996.
(31) Abundance of hyperbolicity in the C topology, Annales Scientififiques de L’Ecole Normale Superieure, quatri´eme s´erie, t. 28, p. 747-760, 1995.
(32) On the approximation of H´enon-like attractors by homoclinic tangencies, Ergodic Theory and Dynamical Systems, Vol. 15, p. 1223-1229, 1995.
(33) Persistent homoclinic tangencies and the unfolding of cycles, joint with L.J. D´ıaz, Annales de l’Institut Henri Poincar´e, Vol. 11, no. 6, p. 643-659, 1994.
Academic books
(34) Partially hyperbolic dynamics, joint with F. Rodriguez Hertz and M. A. Rodriguez Hertz, Col´oquio Brasileiro de Matem´atica, IMPA, Brasil, 2011.
