Books Edited


  1. Some aspects of the theory of dynamical systems: a tribute to Jean-Christophe Yoccoz (Volume I and Volume II), edited with Sylvain Crovisier, Raphaël Krikorian and Samuel Senti.  Astérisque (2020).

Habilitation (HDR):


    Dynamical Systems and Ergodic Theory
  1. Quelques contributions à la théorie de l'action de \( SL(2,\mathbb{R}) \) sur les espaces de modules de surfaces plates. This memoir (in english) is my Habilitation, Université Paris 13 (2016).

Expository Articles:


    Dynamical Systems
  1. Renormalisation en Systèmes Dynamiques, article written for the journal  Gazette des Mathématiciens (Publication of the French Mathematical Society), vol.180, p. 22-35 (April 2024).
    2. Dynamical Systems
  2. Three lectures in square tiled surfaces - article written for the collection Panoramas et Synthèses, vol. 58, 77-99 (2022).
    3. Dynamical Systems and Number Theory
  3. Diophantine approximations, Markov and Lagrange spectra and dynamical Cantor sets,  joint with Carlos Gustavo Moreira, Notices of the American Mathematical Society,  1301-1311, September 2021. 
    4. Dynamical Systems and Analysis
  4. Some variants of Orponen's theorem on visible parts of fractal sets, article written for the book Thermodynamic Formalism , CIRM Jean-Morlet Chair Subseries, Fall 2019, Springer Verlag, 517-533 (2021).
    5. Dynamical Systems
  5. On the dynamics on the \(SU(2)\)-character variety of a once-punctured torus, Actes du Séminaire de Théorie Spectrale et Géométrie of the Institut Fourier in Grenoble, vol. 36 (2018-2019).
    6. Dynamical Systems and Number Theory
  6. The rich geometry of the Lagrange and Markov spectra, article published in the series Séminaire et Congrès, vol. 33, 155-164, Société Mathématique de France (2019).
    7. Dynamical Systems and Number Theory
  7. The Lagrange and Markov spectra from the dynamical point of view, article written for the book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics, CIRM Jean-Morlet Chair Subseries, Fall 2016, Lect. Notes Math. 2213,  259-291, Springer Verlag (2018).
    8. Dynamical Systems and Geometry
  8. Lecture notes on the dynamics of the Weil-Petersson flow, article written for the book Ergodic theory and negative curvature, CIRM Jean-Morlet Chair Subseries, Fall 2013, B. Hasselblatt ed, Lect. Notes Math. 2164,  209-291, Springer Verlag (2017).
    9. Dynamical Systems and Geometry
  9. Ergodicity of Geodesic Flows on Incomplete Negatively Curved Manifolds, joint with Keith Burns,  Howard Masur  and  Amie Wilkinson,   article written for the book Ergodic theory and negative curvature, CIRM Jean-Morlet Chair Subseries, Fall 2013, B. Hasselblatt ed, Lect. Notes Math. 2164,  175-208, Springer Verlag (2017).
    10. Dynamical Systems and Ergodic Theory
  10. Variations of Hodge structures, Lyapunov exponents and Kontsevich’s formula , appendix of the book Gauss-Manin Connection in Disguise: Calabi-Yau Modular Forms, written by Hossein Movasati,  Surveys of Modern Mathematics, vol. 13  (April 2017).
    11. Math Blogs
  11. Les blogs : un outil dynamique de communication en mathématiques, article written for the journal  Gazette des Mathématiciens (Publication of the French Mathematical Society), vol.148, p. 46-50 (April 2016).
    12. Dynamical Systems and Ergodic Theory
  12. A criterium for the simplicity of Lyapunov exponents of origamis, joint with Martin Möller  and  Jean-Christophe Yoccoz , Oberwolfach Reports, vol. 10, p. 1975–2033 (2013).
    13. Dynamical Systems and Ergodic Theory
  13. Fractal geometry of non-uniformly hyperbolic horseshoes , Proceedings of the Ergodic Theory workshops at University of North Carolina at Chapel Hill, p. 197-240 (2011-2012).
    14. Dynamical Systems and Ergodic Theory
  14. Le flot géodésique de Teichmüller et la géométrie du fibré de Hodge , Actes du Séminaire de Théorie Spectrale et Géométrie of the Institut Fourier in Grenoble, vol. 29, p. 73-95 (2010-2011).
    15. Dynamical Systems and Ergodic Theory
  15. On the neutral Oseledets bundle of Kontsevich-Zorich cocycle over certain cyclic covers , joint with Giovanni Forni  and  Anton Zorich,  Oberwolfach Reports, vol. 8,  p. 1361–1427 (2011).
    16. Dynamical Systems and Ergodic Theory
  16. \(C^1\)density of hyperbolicity for Benedicks-Carleson toy models, joint with C. G. Moreira and E. Pujals, Oberwolfach Reports, vol. 6, p. 1819- 1823 (2009).
    17. Dynamical Systems and Ergodic Theory
  17. An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum, joint with Giovanni Forni, 2008 (not intended for publication).
    18. Geometry
  18. O trabalho de Ennio De Giorgi sobre o problema de Plateau (in portuguese), joint with A. Arbieto and K. Oliveira,   Revista Matemática Universitária, n. 35 (december 2003), 1-29.

Some Special Colloquiums


  1. Encontro Nacional SPM 2021,  Portugal (2021).
  2. Rankin Lecture: Billiards,  University of Glasgow, Scotland (2020).
  3. Deux mathématiciens à la recherche de l’harmonie et du chaos: hommage à Michael Herman et Jean-Christophe Yoccoz , Académie des sciences, Paris, France (2019).
  4. Colloquium Series: Counting periodic trajectories in Sinai billiards,  UCD School of Mathematics and Statistics, Dublin, Ireland (2018).