Math documents (Most of them are in Spanish):

Structure of quasi-attractors and existence of attractors in C1-generic dynamics. Expanded notes (in “french”) of a talk given at Paris 11 (June 2011).

Blenders and Robust transitivity. Preliminary Version (April 2010)

Katok’s Theorem on the existence of horseshoes in surfaces. (Abril 2010)

Oseledet’s Theorem in Dimension 2. Notes based on other notes by Avila and Bochi (March 2010)

Closing Lemma Ergódico A simpler proof of the Ergodic Closing Lemma given by Sylvain Crovisier (December de 2009)

Conos y dominación A review on the relationship between cones and domination. (November 2009).

Prueba del Teorema de la Variedad Estable en dimensión 2. A proof of the stable manifold theorem in dimensión 2(November 2009)

Prueba elemental del Teorema de invariancia de la dimensión. A simple proof of the invariance of dimensión theorem. The topological tool used is mod 2 degree for diferentiable maps and aproximation of continuous functions by differentiable ones. (June 2009)

Existencia de intersecciones homoclinicas lejos de los Morse-Smale. Notes for an informal seminar on Crovisier’s proof of the weak Palis conjecture (November 2008)

Clases homoclínicas genéricas con interior. My master’s thesis on homoclinic classes with non empty interior for generic diffeomorphisms (August 2008)

Resumen de mi tesis de maestria. Brief notes on my master’s thesis (June 2008).

Flujo geodésico de Anosov y en variedades sin puntos conjugados, Notes on Anosov geodesic flows and geodesic flows on manifolds without conjugate points. A simple proof of the non existence of transversals for geodesic flows on surface is given (due to Matilde Martinez and Alberto Verjovsky) (November 2008).

Sistemas Dinámicos Expansivos, Brief survey on expansive homeomorphisms on manifolds. Some simple theorems are proved and then the known results are presented (March 2007).

Transitividad Robusta en Superficies, My degree’s monograph. I give here a proof of the fact that robustly transitive diffeomorphisms of surfaces are conjugated to Anosov diffeomorphisms. The proof is self contained (except from the use of Pugh’s closing lemma) and doesn´t use the Ergodic Closing Lemma (March 2007)

Lema de Pliss A proof of Pliss Lemma (January 2007)

Herradura de Smale Smale’s horseshoe (January 2007)

Estabilidad Casi Global  Notes on Almost global stability of differential equations (March 2007)

Construcciones con regla y compás Unfinished. A proof of the fact that some numbers cannot be reached by constructions with compas and ruler (Novembre 2006)

Notas de Numerabilidad Notes on countability for a course of elementary calculus (March 2005)