Articles:

     
    Dynamical Systems and Number Theory
  1. Fractal geometry of the complement of Lagrange spectrum in Markov spectrum, joint with Carlos Gustavo MoreiraCommentarii Mathematici Helvetici (2019).
  2. Dynamical Systems
  3. Stable sets of certain non-uniformly hyperbolic horseshoes have the expected dimension, joint with  Jacob Palis and Jean-Christophe Yoccoz, Journal of the Inst. of Math. of Jussieu (2019).
  4. Dynamical Systems
  5. An origami of genus 3 with arithmetic Kontsevich-Zorich monodromy, joint with Pascal HubertMathematical Proceedings of the Cambridge Philosophical Society (2019).
  6. Dynamical Systems
  7. Cohomological equation and local conjugacy class of Diophantine interval exchange maps, joint with Giovanni Forni and Stefano Marmi, Proceedings of the AMS (2019).
  8. Dynamical Systems and Ergodic Theory
  9. Semisimplicity of the Lyapunov spectrum for irreducible cocycles, joint with  Alex Eskin, Israel Journal of Mathematics, vol. 230, 973 - 1005 (2019).
  10. Dynamical Systems and Geometric Group Theory
  11. The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces, joint with Artur Avila  and  Jean-Christophe Yoccoz, Journal of Modern Dynamics, Veech Special volume, vol. 14, 21-54 (2019).
  12. Dynamical Systems and Number Theory
  13. Markov spectrum near Freiman's isolated points in M-L, joint with Carlos Gustavo Moreira,   Journal of Number Theory, vol. 194, 390-408 (2019).
  14. Dynamical Systems and Number Theory
  15. HD(M-L) > 0.353, joint with Carlos Gustavo Moreira, Acta Arithmetica, vol. 188, 183-208 (2019).
  16. Dynamical Systems and Algebraic Geometry
  17. Appendix On special Lagrangian fibrations in generic twistor families of K3 surfaces, joint with Nicolas Bergeron,  to Simion Filip's paper Counting Special Lagrangian Fibrations in Twistor Families of K3 surfaces, Annales scientifiques de l'ENS (2018).
  18. Dynamical Systems and Number Theory
  19. Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra, joint with Aline Cerqueira and Carlos Gustavo MoreiraJournal of Modern Dynamics ,  vol. 12, 151-174 (2018).
  20. Dynamical Systems and Ergodic Theory
  21. Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases, joint with Mario Bessa, Jairo Bochi, Michel Cambrainha, Paulo Varandas and Disheng XuBoletim da SBM, vol. 49, no. 1, 73-87 (2018).
  22. Dynamical Systems and Ergodic Theory
  23. Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities,  joint with  Yuri LimaAnnales de l'ENS, vol. 51, no. 1, 1-38 (2018).
  24. Dynamical Systems and Ergodic Theory
  25. Zorich conjecture for hyperelliptic Rauzy-Veech groups, joint with Artur Avila  and  Jean-Christophe Yoccoz, Mathematische Annalen, vol. 370, 785–809 (2018) .
  26. Dynamical Systems
  27. Non-uniformly hyperbolic horseshoes in the standard family, joint with Carlos Gustavo Moreira and Jacob PalisComptes Rendus de l'Académie des Sciences, vol. 356, no. 2, 146-149 (2018).
  28. Dynamical Systems and Ergodic Theory
  29. Quaternionic covers and monodromy of the Kontsevich-Zorich cocycle in orthogonal groups, joint with Giovanni Forni and Simion Filip, Journal of the European Mathematical Society, vol. 20, no. 1, 165 - 198 (2018).
  30. Dynamical Systems
  31. An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes, joint with Jacob Palis, Discrete and Continuous Dynamical Systems, vol. 38,  no. 2,  431 - 448 (2018). 
  32. Dynamical Systems, Ergodic Theory and Differential geometry
  33. Rates of mixing for the Weil-Petersson geodesic flow II: exponential mixing in exceptional moduli spaces,  joint with  Keith BurnsHoward Masur  and  Amie WilkinsonGeometric and Functional Analysis, vol. 27, no. 2, 240–288 (2017). There is a supplementary paper with some calculations that justifies the statements of the Lemma 4.8 and the Proposition 4.10. You can see here: Calculating the \( \star \) connection.
  34. Dynamical Systems and Ergodic Theory
  35. Rates of mixing for the Weil-Petersson geodesic flow I: no rapid mixing in non-exceptional moduli spaces, joint with Keith BurnsHoward Masur  and  Amie Wilkinson, Advances in Mathematics, vol. 306, 589-602 (2017).
  36. Dynamical Systems and Ergodic Theory
  37. Typical symplectic locally constant cocycles over certain shifts of countable type have simple Lyapunov spectra, joint with Michel CambrainhaPortugaliae Mathematica, vol. 73,  no. 3, 171-176 (2016).
  38. Dynamical Systems and Ergodic Theory
  39. A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves, joint with  Alex EskinGeometriae Dedicata, vol. 179, no. 1,  45-67 (2015).
  40. Dynamical Systems, Ergodic Theory and Algebraic Geometry
  41. A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces, joint with Martin Möller  and  Jean-Christophe Yoccoz, Inventiones mathematicae, vol. 202, no. 1, 333-425 (2015). 
  42. Dynamical Systems and Ergodic Theory
  43. Some examples of isotropic \(SL(2,\Bbb{R})\)-invariant subbundles of the Hodge bundle, joint with  Gabriela Weitze-SchmithüsenInternational Mathematics Research Notices, vol. 2015, no.18, 8657-8679 (2015).
  44. Dynamical Systems and Ergodic Theory
  45. Hodge-Teichmueller planes and finiteness results for Teichmueller curves, joint with  Alex WrightDuke Mathematical Journal, vol. 164, no. 6, 1041-1077 (2015).
  46. Dynamical Systems and Ergodic Theory
  47. Un contre-exemple à la réciproque du critère de Forni pour la positivité des exposants  de  Lyapunov  du  cocycle  de  Kontsevich-Zorich, joint with  Vincent DelecroixMathematical Research Letters, vol. 22, no. 6, 1667 - 1678 (2015).
  48. Dynamical Systems and Ergodic Theory
  49. Zero Lyapunov exponents of the Hodge bundle, joint with  Giovanni Forni and  Anton Zorich, Commentarii Mathematici Helvetici, vol. 89, no. 2, 489–535 (2014). You can see the Mathematica routine used  here
  50. Dynamical Systems and Ergodic Theory
  51. Lyapunov spectrum of invariant subbundles of the Hodge bundle, joint with  Giovanni Forni and Anton Zorich,  Ergodic Theory and Dynamical Systems, vol. 34, no. 2, 353-408 (2014).
  52. Dynamical Systems, Ergodic Theory and Representation Theory
  53. Homology of origamis with symmetries , joint with  Jean-Christophe Yoccoz and David ZmiaikouAnnales de l´Institut Fourier,  vol.64, no. 3, 1131-1176 (2014). There is a  Corrigendum.
  54. Dynamical Systems and Ergodic Theory
  55. Explicit Teichmüller curves with complementary series, joint with  Gabriela Weitze-SchmithüsenBoletim da SMF, vol. 141, no. 4 , 557-602 (2013) .
  56. Dynamical Systems and Ergodic Theory
  57. \(SL(2,\Bbb{R})\)-invariant probability measures on the moduli spaces of translation surfaces are regular, joint with  Artur Avila and Jean-Christophe YoccozGeometric and Functional Analysis, vol. 23, no. 6, 1705-1729 (2013).  See here (1080p | 480p | 240p)  a video about this article.
  58. Dynamical Systems
  59. Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models, joint with Carlos Gustavo Moreira and Enrique PujalsAnnales de l'ENS, vol. 46, no. 6,  857-878 (2013).
  60. Dynamical Systems and Ergodic Theory
  61. Some quantitative versions of Ratner’s mixing estimates, Boletim da SBM, vol.44, no.3, 469-488 (2013).
  62. Dynamical Systems and Ergodic Theory
  63. Appendix Other relevant examples to Giovanni Forni's paper A geometric criterion for the non-uniform hyperbolicity of the Kontsevich-Zorich cocycle,  Journal of Modern Dynamics, vol. 5,  no.2,   355 - 395 (2011).
  64. Dynamical Systems and Ergodic Theory
  65. Square-tiled cyclic covers, joint with Giovanni Forni and Anton ZorichJournal of Modern Dynamics, vol. 5,  no.2,  285 - 318 (2011).
  66. Dynamical Systems and Ergodic Theory
  67. The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis, joint with Jean-Christophe YoccozJournal of Modern Dynamics, vol. 4, no.3, 453-486 (2010).
  68. Analysis
  69. Well-posedness for the 1D Zakharov-Rubenchik system, joint with Felipe Linares,  Advances in Differential Equations, vol. 14, n.3-4, 261-288 (2009).
  70. Analysis
  71. Sharp bilinear estimates and well-posedness for the 1D Schrödinger - Debye system, joint with Adán Corcho,  Differential and Integral Equations , vol. 22, n.3-4, 357-391 (2009).
  72. Analysis
  73. Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system , joint with Jaime Angulo and Didier Pilod,  Communications in Pure and Applied Analysis, vol. 8, n.3, 815-844 (2009).
  74. Analysis
  75. On the periodic Schrödinger-Debye equation, joint with A. Arbieto,  Communications on Pure and Applied Analysis, vol. 7, 699-713 (2008).
  76. Analysis
  77. Global well-posedness of NLS-KdV systems for periodic functions, Electronic Journal of Differential Equations , vol. 2007, n. 7, 1-20 (2007).
  78. Dynamical Systems and Ergodic Theory
  79. A pasting lemma and some applications for conservative systems (a.k.a. "A pasting lemma I: the vector field case"), joint with A. Arbieto,  Ergodic Theory and Dynamical Systems, vol. 27, 1399-1417 (2007).  There is a Corrigendum.
  80. Analysis
  81. Rough solutions for the periodic Schrödinger - Korteweg-deVries system, joint with A. Arbieto and Adán Corcho,  Journal of Differential Equations, vol. 230, 295-336 (2006).
  82. Geometry and Topology
  83. Geometrical versus Topological properties of manifolds, joint with Krerley Oliveira,  Journal of the Institute of Mathematics of Jussieu, vol. 4, 639-651 (2005).
  84. Dynamical Systems and Ergodic Theory
  85. The Bernoulli property for weakly hyperbolic systems, joint with A. Arbieto and M. PacíficoJournal of Statistical Physics, vol. 117, 243-260 (2004).
  86. Geometry
  87. Immersions with fractal sets of points of zero Gauss-Kronecker curvature, joint with A. ArbietoBulletin of the Brazilian Mathematical Society, vol. 35, 363-376 (2004).
  88. Dynamical Systems and Ergodic Theory
  89. Equilibrium states for random non-uniformly expanding maps, joint with A. Arbieto and K. Oliveira,   Nonlinearity, vol. 17, 581-593 (2004).
  90. Dynamical Systems and Ergodic Theory
  91. Abundance of stable ergodicity, joint with C. BonattiM. Viana and A. WilkinsonCommentarii Mathematici Helvetici, vol.79, 753-757 (2004).
  92. Dynamical Systems and Ergodic Theory
  93. Decidability of chaos for some families of dynamical systems, joint with A. ArbietoFoundations  of  Computational  Mathematics, vol. 4, 269-275 (2004).