Articles:

     
    Dynamical Systems
  1. Appendix Lyapunov exponents and weak-mixing for S-adic systems , joint with Pascal Hubert,  to Boris Solomyak's paper A note on spectral properties of random S-adic systems,  Pure and Applied Functional Analysis dedicated to the memory of A. M. Vershik (2024).
    2. Dynamical Systems
  2. Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces, joint with Etienne Bonnafoux, Manuel Kany, Pascal Kattler, Rogelio Niño, Manuel Sedano-Mendoza, Ferrán Valdez and Gabriela Weitze-Schmithüsen,  Transactions of the AMS (2024).
    3. Dynamical Systems
  3. Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus, joint with Giovanni Forni, William Goldman and Sean Lawton, Annales Henri Lebesgue, vol. 7, 1099-1130 (2024).
    4. Dynamical Systems and Geometry
  4. Polynomial decay of correlations for nonpositively curved surfaces, com Yuri Lima and Ian Melbourne, Transactions of the AMS, vol. 377, issue 9, 6043-6095 (2024).
    5. Dynamical Systems and Number Theory
  5. New gaps on the Lagrange and Markov spectra, joint with Luke Jeffreys and Carlos Gustavo Moreira, Journal de Théorie des Nombres de Bordeaux, vol. 36, issue 1, 311-338 (2024).
    6. Dynamical Systems
  6. Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces II,  joint with Manuel Kany, Mathematische Nachrichten , vol. 297, issue 5, 1892-1921 (2024).
    7. Algebraic Geometry
  7. Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials, joint with Bertrand Deroin,  Comptes Rendus de l'Académie des Sciences, vol. 361, 1691-1698 (2023).
    8. Dynamical Systems
  8. Non-planarity of \(SL(2,\Bbb{Z})\)-orbits of origamis in \(\mathcal{H}(2)\), joint with Luke Jeffreys, Bulletin of the London Mathematical Society, vol. 55, issue 5, 2258-2269 (2023).
    9. Dynamical Systems and Number Theory
  9. Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra, joint with Carlos Gustavo Moreira, Mark Pollicott and Polina Vytnova, Advances in Mathematics, vol. 409, part B, article 108693 (2022).
    10. Dynamical Systems and Geometry
  10. Cusp excursions of random geodesics in Weil-Petersson type metrics, joint with Vaibhav Gadre, Journal of Differential Geometry, vol. 121, issue 1, 31-55 (2022).
    11. Number Theory
  11. \(M \setminus L\) is not closed, joint with Davi Lima, Carlos Gustavo Moreira and Sandoel Vieira,  International Mathematics Research Notices, vol. 2022, issue 1, 265-311 (2022).
    12. Number Theory
  12. \(M \setminus L\) near 3, joint with Davi Lima, Carlos Gustavo Moreira and Sandoel Vieira,  Moscow Mathematical Journal, vol. 21,  issue 4, 767-788 (2021).
    13. Dynamical Systems
  13. 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, vol. 20, issue 1, 305-329 (2021).
    14. Dynamical Systems and Number Theory
  14. Fractal geometry of the complement of Lagrange spectrum in Markov spectrum, joint with Carlos Gustavo Moreira,  Commentarii Mathematici Helvetici, vol. 95, issue 3, 593-633 (2020).
    15. Dynamical Systems
  15. The beginning of the Lagrange spectrum of certain origamis of genus two,  Comptes Rendus de l'Académie des Sciences, vol. 358, issue 4, 475-479 (2020).
    16. Dynamical Systems
  16. An origami of genus 3 with arithmetic Kontsevich-Zorich monodromy, joint with Pascal Hubert, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 169, issue 1, 19-30 (2020).
    17. Dynamical Systems and Computer Science
  17. Approximations of the Lagrange and Markov spectra, joint with  Vincent Delecroix and Carlos Gustavo Moreira, Mathematics of Computation, vol. 89, issue 325, 2521-2536 (2020).
    18. Dynamical Systems
  18. Lower bounds on the dimension of the Rauzy gasket, joint with Rodolfo Gutiérrez-Romo,  Bulletin de la SMF, vol. 148, issue 2, 321-327 (2020).
    19. Dynamical Systems and Algebraic Geometry
  19. 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, vol. 53, 713-750 (2020).
    20. Dynamical Systems
  20. Cohomological equation and local conjugacy class of Diophantine interval exchange maps, joint with Giovanni Forni and Stefano Marmi, Proceedings of the AMS (accepted 2019).
    21. Dynamical Systems and Ergodic Theory
  21. Semisimplicity of the Lyapunov spectrum for irreducible cocycles, joint with  Alex Eskin, Israel Journal of Mathematics, vol. 230, 973-1005 (2019).
    22. Dynamical Systems and Geometric Group Theory
  22. 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).
    23. Dynamical Systems and Number Theory
  23. Markov spectrum near Freiman's isolated points in M-L, joint with Carlos Gustavo Moreira,   Journal of Number Theory, vol. 194, 390-408 (2019).
    24. Dynamical Systems and Number Theory
  24. HD(M-L) > 0.353, joint with Carlos Gustavo Moreira, Acta Arithmetica, vol. 188, 183-208 (2019).
    25. Dynamical Systems and Number Theory
  25. Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra, joint with Aline Cerqueira and Carlos Gustavo Moreira, Journal of Modern Dynamics ,  vol. 12, 151-174 (2018).
    26. Dynamical Systems and Ergodic Theory
  26. 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 Xu,  Boletim da SBM, vol. 49, no. 1, 73-87 (2018).
    27. Dynamical Systems and Ergodic Theory
  27. Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities,  joint with  Yuri Lima,  Annales de l'ENS, vol. 51, no. 1, 1-38 (2018).
    28. Dynamical Systems and Ergodic Theory
  28. Zorich conjecture for hyperelliptic Rauzy-Veech groups, joint with Artur Avila  and  Jean-Christophe Yoccoz, Mathematische Annalen, vol. 370, 785–809 (2018) .
    29. Dynamical Systems
  29. Non-uniformly hyperbolic horseshoes in the standard family, joint with Carlos Gustavo Moreira and Jacob Palis,  Comptes Rendus de l'Académie des Sciences, vol. 356, no. 2, 146-149 (2018).
    30. Dynamical Systems and Ergodic Theory
  30. 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).
    31. 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
  32. Rates of mixing for the Weil-Petersson geodesic flow II: exponential mixing in exceptional moduli spaces,  joint with  Keith Burns,  Howard Masur  and  Amie Wilkinson, Geometric 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.
    33. Dynamical Systems and Ergodic Theory
  33. Rates of mixing for the Weil-Petersson geodesic flow I: no rapid mixing in non-exceptional moduli spaces, joint with Keith Burns,  Howard Masur  and  Amie Wilkinson, Advances in Mathematics, vol. 306, 589-602 (2017).
    34. Dynamical Systems and Ergodic Theory
  34. Typical symplectic locally constant cocycles over certain shifts of countable type have simple Lyapunov spectra, joint with Michel Cambrainha,  Portugaliae Mathematica, vol. 73,  no. 3, 171-176 (2016).
    35. Dynamical Systems and Ergodic Theory
  35. A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves, joint with  Alex Eskin, Geometriae Dedicata, vol. 179, no. 1,  45-67 (2015).
    36. Dynamical Systems, Ergodic Theory and Algebraic Geometry
  36. 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). 
    37. Dynamical Systems and Ergodic Theory
  37. Some examples of isotropic \(SL(2,\Bbb{R})\)-invariant subbundles of the Hodge bundle, joint with  Gabriela Weitze-Schmithüsen,  International Mathematics Research Notices, vol. 2015, no.18, 8657-8679 (2015).
    38. Dynamical Systems and Ergodic Theory
  38. Hodge-Teichmueller planes and finiteness results for Teichmueller curves, joint with  Alex Wright,  Duke Mathematical Journal, vol. 164, no. 6, 1041-1077 (2015).
    39. Dynamical Systems and Ergodic Theory
  39. 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 Delecroix, Mathematical Research Letters, vol. 22, no. 6, 1667 - 1678 (2015).
    40. Dynamical Systems and Ergodic Theory
  40. 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. 
    41. Dynamical Systems and Ergodic Theory
  41. 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).
    42. Dynamical Systems, Ergodic Theory and Representation Theory
  42. Homology of origamis with symmetries , joint with  Jean-Christophe Yoccoz and David Zmiaikou,  Annales de l´Institut Fourier,  vol.64, no. 3, 1131-1176 (2014). There is a  Corrigendum.
    43. Dynamical Systems and Ergodic Theory
  43. Explicit Teichmüller curves with complementary series, joint with  Gabriela Weitze-Schmithüsen,  Bulletin de la SMF, vol. 141, no. 4 , 557-602 (2013) .
    44. Dynamical Systems and Ergodic Theory
  44. \(SL(2,\Bbb{R})\)-invariant probability measures on the moduli spaces of translation surfaces are regular, joint with  Artur Avila and Jean-Christophe Yoccoz, Geometric and Functional Analysis, vol. 23, no. 6, 1705-1729 (2013).  See here (1080p | 480p | 240p)  a video about this article.
    45. Dynamical Systems
  45. Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models, joint with Carlos Gustavo Moreira and Enrique Pujals,  Annales de l'ENS, vol. 46, no. 6,  857-878 (2013).
    46. Dynamical Systems and Ergodic Theory
  46. Some quantitative versions of Ratner’s mixing estimates, Boletim da SBM, vol.44, no.3, 469-488 (2013).
    47. Dynamical Systems and Ergodic Theory
  47. 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).
    48. Dynamical Systems and Ergodic Theory
  48. Square-tiled cyclic covers, joint with Giovanni Forni and Anton Zorich,  Journal of Modern Dynamics, vol. 5,  no.2,  285 - 318 (2011).
    49. Dynamical Systems and Ergodic Theory
  49. The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis, joint with Jean-Christophe Yoccoz,  Journal of Modern Dynamics, vol. 4, no.3, 453-486 (2010).
    50. Analysis
  50. Well-posedness for the 1D Zakharov-Rubenchik system, joint with Felipe Linares,  Advances in Differential Equations, vol. 14, n.3-4, 261-288 (2009).
    51. Analysis
  51. 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).
    52. Analysis
  52. 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).
    53. Analysis
  53. On the periodic Schrödinger-Debye equation, joint with A. Arbieto,  Communications on Pure and Applied Analysis, vol. 7, 699-713 (2008).
    54. Analysis
  54. Global well-posedness of NLS-KdV systems for periodic functions, Electronic Journal of Differential Equations , vol. 2007, n. 7, 1-20 (2007).
    55. Dynamical Systems and Ergodic Theory
  55. 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.
    56. Analysis
  56. 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).
    57. Geometry and Topology
  57. Geometrical versus Topological properties of manifolds, joint with Krerley Oliveira,  Journal of the Institute of Mathematics of Jussieu, vol. 4, 639-651 (2005).
    58. Dynamical Systems and Ergodic Theory
  58. The Bernoulli property for weakly hyperbolic systems, joint with A. Arbieto and M. Pacífico,  Journal of Statistical Physics, vol. 117, 243-260 (2004).
    59. Geometry
  59. Immersions with fractal sets of points of zero Gauss-Kronecker curvature, joint with A. Arbieto, Bulletin of the Brazilian Mathematical Society, vol. 35, 363-376 (2004).
    60. Dynamical Systems and Ergodic Theory
  60. Equilibrium states for random non-uniformly expanding maps, joint with A. Arbieto and K. Oliveira,   Nonlinearity, vol. 17, 581-593 (2004).
    61. Dynamical Systems and Ergodic Theory
  61. Abundance of stable ergodicity, joint with C. Bonatti,  M. Viana and A. Wilkinson,  Commentarii Mathematici Helvetici, vol.79, 753-757 (2004).
    62. Dynamical Systems and Ergodic Theory
  62. Decidability of chaos for some families of dynamical systems, joint with A. Arbieto,  Foundations  of  Computational  Mathematics, vol. 4, 269-275 (2004).