Mi preprints are available at arXiv and PreMat

My research interests include: Differentiable and topological dynamics, Geometric topology and Foliations. In non-technical language, the relationship between shape and movement.

Pre-prints and work in progress:

"Classification of partially hyperbolic diffeomorphisms in 3-manifolds with solvable fundamental group" with A. Hammerlindl (2013) Preprint. Submitted.

 

Published and accepted papers (the preprint versions below may differ from the published versions):

"A few remarks on partially hyperbolic diffeomorphisms of T3 isotopic to Anosov" (2013) Preprint. To appear in Journal of Dynamics and Differential Equations.   

"Dynamical coherence for partially hyperbolic diffeomorphisms of tori isotopic to Anosov" with T. Fisher and M. Sambarino. Preprint. To appear in Math. Z.

"Pointwise partial hyperbolicity in 3-dimensional nilmanifolds" with. A.Hammerlindl  Journal of the London Math. Society . 89 n3 (2014) 853-875  (Preprint.)  

“Partial hyperbolicity and foliations in T^3” Preprint. To appear in Journal of Modern Dynamics.

“Tame dynamics and robust transitivity” with C. Bonatti, S. Crovisier and N. Gourmelon,   Transactions of the AMS 366 n9 (2014) 4849-4871.  preprint.

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

"On the work of Jorge Lewowicz on expansive homeomorphisms"  Publicaciones Matemáticas del Uruguay 14 (2013)   6-22 ( Preprint )

“Recurrence of non-resonant torus homeomorphisms” preprint.  Proceedings of the A.M.S. 140 (2012), 3973-3981 

“Generic bi-Lyapunov stable homoclinic classes” Nonlinearity, 23 (2010) 1631-1650. preprint.

"Codimension one generic homoclinic classes with interior" with M. Sambarino.  Bulletin of the Brazilian Math Society NS 41 (2010)  125-138. Preprint .

"Local implications of almost global stability" with P.Monzón. Dynamical Systems: An International Journal vol  24(2009) p.109-115. Preprint.

“Local Product Structure for Expansive Homeomorphisms” with A. Artigue y J. Brum. Topology and its Applications vol 156(2009) p.674-685.  Preprint.

"Local and global aspects of almost global stability" with  P.Monzón. Proceedings of the 45th IEEE CDC (2006) 

 

Permanent preprints, not intended for publication.

"Entropia y Topologia" Lecture notes for minicourse on the entropy conjecture given at Montevideo March-April 2014.

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

“Non existence of attractors and dynamics around some wild homoclinic classes”  preprint in arXiv. (2010) Previous version of “Wild Milnor attractors accumulated by lower dimensional dynamics”.

“A proof of the existence of attractors in dimension two” Preprint, Not intended for publication (2009).

Monographs:

Tesis de doctorado: "Partial hyperbolicity and attracting regions in 3-dimensional manifolds" Tesis de doctorado: Defended on 3rd July 2012 under the supervision of Sylvain Crovisier and Martín Sambarino. Buy a copy here.

Tesis de Maestría "Clases homoclínicas genéricas con interior". MASTER THESIS  Defended on the 13 of August  2008 under the supervision of Martín Sambarino.

Monografía de Licenciatura "Transitividad robusta en superficies" DEGREE MONOGRAPH Defended on the 2 of March 2007 under the supervision of Martín Sambarino.

 

Slides/Posters/Talks:

"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 University Dynamical 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 also Andy'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” Pucón 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).

 

 

If you wish to have some source file, write me at rpotrie(AT)cmat.edu.uy