Pierre-Antoine Guihéneuf

Preprints

• 2025 Surface homeomorphisms with big rotation set.
• 2025 A rotational hyperbolic theory for surface homeomorphisms.
• 2025 Bounded deviations in higher genus I: closed geodesics, with Fabio Tal.
• 2025 Bounded deviations in higher genus II: minimal laminations, with Fabio Tal.
• 2023 Geodesic tracking and the shape of ergodic rotation sets, with Alejo Garcia and Pablo Lessa.

Published articles

• 2023 Hyperbolic isometries of the fine curve graph of higher genus surfaces, with Emmanuel Militon, to appear in Commentarii Mathematici Helvetici.
• 2023 Area preserving homeomorphisms of surfaces with rational rotational direction, with Patrice Le Calvez and Alejandro Passeggi,
  Ann. Henri Lebesgue 8, 329-372 (2025).
• 2023 Parabolic isometries of the fine curve graph of the torus, with Emmanuel Militon,
  Proc. Lond. Math. Soc. (3) 129, No. 2, 27 p. (2024).
• 2022 Cramér distance and discretizations of circle expanding maps I: theory, with Maurizio Monge (UFRJ, Rio de Janeiro),
  Nonlinearity 36, No. 9, 4810-4843 (2023),
  and its second part (which can be read independently) :
• 2022 Cramér distance and discretizations of circle expanding maps II: simulations, with Maurizio Monge,
  Dynamical Systems 39, No. 1, 108-140 (2024).
• 2022 La Homotopic rotation sets for higher genus surfaces, with Emmanuel Militon,
  Memoirs of the AMS 1593, 110 p. (2025).
• 2020 Historic behaviour vs. physical measures for irrational flows with multiple stopping points, with Martin Anderson (UFF),
  Advances in Mathematics, 709 A, 71 p., 108626, (2022).
  A talk about this paper.
• 2019 Dirac physical measures on saddle-type fixed points, with Pablo Guarino and Bruno Santiago,
  Journal of Dynamics and Differential Equations 34, p. 983–1048 (2022).
• 2019 Dynamical behavior of a nondiffusive scheme for the advection equation, with Nina Aguillon,
  Confluentes Matematici 12 (2020) no. 1, 3-29.
• 2017 Stability of the rotation set of area-preserving toral homeomorphisms, with Andres Koropecki,
  Nonlinearity 30 (2017), no. 3, 1089-1096.
• 2016 On the genericity of the shadowing property for conservative homeomorphisms, with Thibault Lefeuvre,
  Proceedings of the AMS 146 (2018), no. 10, 4225-4237.
• 2016 A Minkowski theorem for Meyer sets, with Emilien Joly,
  Discrete & Computational Geometry 58 (2017), iss. 3, 596-613.
• 2015 Model sets, almost periodic patterns, uniform density and linear maps,
  Revista Matemática Iberoamericana 34 (2018), no. 1, 455-474.
• 2015 Degree of recurrence of generic diffeomorphisms
  Discrete Analysis (2019).
• 2015 Physical measures of discretizations of generic diffeomorphisms,
  Ergodic Theory and Dynamical Systems 38 (2018), no. 4, 1422-1458.
• 2015 Discretizations of isometries,
  Lecture Notes in Computer Science (proceedings de la conférence DGCI 2016).
• 2014 How roundoff errors help to compute the rotation set of torus homeomorphisms,
  Topology and its Applications 193 (2015), 116-139.
• 2013 Dynamical properties of spatial discretizations of a generic homeomorphism,
  Ergodic Theory and Dynamical Systems 35 (2015), no. 5, 1474-1523.
  An addendum to this paper, some simulations relatives and a poster around this paper.

Permanent preprints

• Instability for the rotation set of diffeomorphisms of the torus homotopic to the identity.
• Almost periodic patterns (collaboration with Yves Meyer, 2014).

Reports

• Théorie de la rotation sur les surfaces, translation soon !
• Théorie de forçage de Le Calvez and Tal, Exposé Bourbaki n°1171
• Between 2011 and 2015, I was PhD student in Orsay under the direction of François Beguin. Here is an updated version of my thesis (the initial version can be found on TEL).
• Propriétés dynamiques génériques des homéomorphismes conservatifs, master thesis published in Ensaios Matematicos 22, 2012. An addendum about the simple spectrum and a short text about the set of periodic points (updated in 04/2021: there was a mistake in the first version).
• Deux applications du théorème de la forme normale de Birkhoff (1st year of master).