Publications

Thesis

PhD Persistance des stratifications de laminations normalement dilatées, Université Paris Sud - XI. directed by Jean-Christophe Yoccoz. Defended on June 22, 2007 HDR Chaotic Properties of differentiable dynamical systems, defended on June 2, 2017, with S. Crovisier (rapporteur interne), F. Ledrappier (rapporteur), M. Lyubich (rapporteur), and with M. Shishikura, D. Turaev, F. Beguin, J. Barral in the jury.

Articles and preprints

P. Berger, Wild dynamics on manifolds, to appear in Proceeding ICM, (2026), 17 p. P. Berger, Analytic pseudo-rotations, to appear in Annals of Mathematics, (2026), 34 p. P. Berger and D. Turaev, On Kolmogorov-typical properties of symplectic dynamics, , arxiv (2025) 27 p. P. Berger, N. Gourmelon and M. Helfter, Every diffeomorphism is a total renormalization of a close to identity map, Inventiones Mathematicae, (2025), p. 28. P. Berger, Analytic pseudo-rotations II: a principle for spheres, disks and annuli, ArXiv, (2024), 34 p. Julia Xénelkis de Hénon, Hénon maps: a list of open problems , Arnold Mathematical Journal , (2024). P. Berger and B. Reinke, Parametric linearization of skew products, accepted for publication in Journal of Modern Dynamics (2022), 24 p. P. Berger and D. Turaev, Generators of groups of Hamiltonian maps, Israel Journal of Math., (2024), 11p. P. Berger, A. Florio and D. Peralta-Salas, Steady Euler Flows on R3 with Wild and Universal Dynamics, Communications in Math. Physics, (2023), p. 1-47. P. Berger, Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface, Journal de l’école polytechnique, (2023) 22 p. P. Berger, S. Crovisier and E. Pujals, Germ-typicality of the coexistence of infinitely many sinks, Advances in Math. (2022) 42 p. P. Berger and S. Biebler, Emergence of wandering stable components, Journal of the American Math. Soc. (2023) 90 p. P. Berger and J. Bochi, On Emergence and Complexity of Ergodic Decompositions , Advances in Mathematics, Vol. 390, (2021) 52 p. P. Berger, Zoology in the Hénon family: twin babies and Milnor's swallows , arxiv (2018) 41 p. P. Berger, Generic family displaying robustly a fast growth of the number of periodic points, Acta Mathematica (2021), 57 p. P. Berger, Complexities of differentiable dynamical systems, Journal of Mathematical Physics, Vol. 61 no3, (2020). P. Berger and D. Turaev, On Herman positive entropy conjecture , Advances in Mathematics, Vol. 349, (2019),p. 1234-1288 P. Berger and J.-C. Yoccoz, Strong regularity, Astérisque, 410 (2019), 14p. P. Berger, Abundance of one dimensional non uniformly hyperbolic attractors for endomorphisms, Astérisque, Vol. 410 (2019) 123 p. P. Berger, Properties of the maximal entropy measure and geometry of Hénon attractors, Journal of the European Mathematical Society, 21 (2019), no. 8, p. 2233--2299 P. Berger, Lectures on structural stability, Dynamical systems, 9–35, Banach Center Publ., 115, Polish Acad. Sci. Inst. Math., Warsaw, (2018). P. Berger, S. Crovisier, E. Pujals, Iterated Functions Systems, Blenders and Parablenders , 13 p Recent Developments in Fractals and Related Fields , (2017). P. Berger, Emergence and non-typicality of the finiteness of the attractors in many topologies , Proceeding of the Steklov inst. (2017) Vol. 297, pp. 1–27. Article translated in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova (2017), Vol. 297, pp. 7–37. P. Berger, Generic family with robustly infinitely many sinks, Corrigendum., Inventiones Matematicae, (2016) 205 : 121. 41p. P. Berger and R. Dujardin, On stability and hyperbolicity for polynomial automorphisms of C^2, Ann. Scient. Ec. Norm. Sup., 4e, 50 , (2017) p447–475 p. P. Berger-C. G. Morreira, Nested Cantor sets , p 1- 18 , Math. Z., 283 (2016), no. 1-2, p. 419 -435. P. Berger and J. De Simoi, On the Hausdorff dimension of Newhouse phenomena, Ann. Henri Poincaré 17 (2016), no. 1, 227-249. P. Berger, Normal forms and Misiurewicz renormalization for dissipative surface endomorphisms, Arxiv (2014) 27 p. M.C. Arnaud and P. Berger, The non-hyperbolicity of irrational invariant curves for twist maps and all that follows, Revista Mat. Iberoamericana n. 32.4 (2016) pp. 1295–1310. P. Berger- A. Kocsard, Structural stability of the inverse limit of endomorphisms, Annales de l'Institut Henri Poincare (C) Non Linear Analysis 34 (5), 1227-1253 (2016). P. Berger- P.D. Carasco, Non uniformly hyperbolic attractors derived from the standard map, Communications in mathematical physics, July (2014) v. 329 1, pp 239-262. P. Berger-A. Rovella, On the inverse limit of endomorphisms , Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol. 30, issue 3, (2013), pp. 463-475. P. Berger- A. Bounemoura, A geometrical proof of the persistence of normally hyperbolic submanifolds, Dynamical systems, 567. Volume: 28. Issue: 4. (2013). P. Berger, A. Laier, L. Velho, An image-space algorithm for immersive views in 3-manifolds and orbifolds, p: 1-12 The Visual Computer, January 18, (2014). P. Berger, Persistence of stratifications of normally expanded laminations , Mémoire de la société mathématique de France, n°134, (2013), 130 p. P. Berger, Persistance des sous-variétés à bord et à coins normalement dilatées, Ann. Inst. Fourier, Grenoble 61, 1 (2011) p. 79-104. P. Berger, Structural stability of attractor-repeller endomorphisms with singularities, Ergodic Theory and Dynamical Systems / Volume 32 / Issue 01 /December (2011) p 1-33. P. Berger, Persistence of laminations, Bull Braz Math Soc, New series, 41 2, (2010) p. 259-319. P. Berger, Persistence of stratifications of normally expanded laminations , in Comptes rendus Mathématique CRAS 346 13 (2008).

Proceedings and outreach articles for mathematicians P. Berger, Analytic pseudo-rotations, Proceeding for Dynamische Systeme congress at MFO (2025). P. Berger, S. Crovisier and E. Pujals, Germ-typicality of Newhouse phenomenon, Proceeding for Dynamische Systeme congress at MFO (2021). P. Berger and S. Biebler, Emergence of wandering stable open components, Proceeding for Dynamische Systeme congress at MFO (2019). P. Berger, Un élève à l’École d’un Maître ,Jean-Christophe Yoccoz numéro spécial de la Gazette des mathématiciens, 6p. April (2018). P. Berger, Persistent bundle over a two dimensional compact set, Proceeding of V Congreso Latinoamericano de Matemáticos, Revista Colombiana de Matemáticas , 25p. (2018). P. Berger, Emergence and para-dynamics, proceeding of the conference in memory to Anosov, 2p. (2016). P. Berger, Esthetopies , Gazette SMF, 2016 P. Berger, Generic family with robustly infinitely many sinks, 1 p Proceeding for Dynamische Systeme congress at MFO (2015). P. Berger, Abundance of one dimensional non uniformly hyperbolic attractors for endomorphisms, Proceeding for Dynamische Systeme congress at MFO (2009), 3 p.

Participation to outreach articles and videos

Co-Author of a scientific article described in Près d’une dynamique stagnante, avec le temps et une loupe, tout peut arriver, Lettre INSMI, 2025 Author of the article Arte multimedia para expresar lo inenarrable de las matemáticas adapted by Ágata A. Timón, Journal El País, March 22nd (2018). Author of the exhibit recorded in Les noces des mathématiques et des arts by Pierre de Parscau, Journal du CNRS, July (2017). Author of the exhibit Esthetopies recorded in a documentary of 15' by Jean-Baptiste Fave, production IHP, July (2017). Author of the exhibit described in La 3D comme vous ne l’avez jamais vue, by Loïc Mangin, magasine Pour la Science, June (2017). Author of a scientific article described in Le chaos est encore plus "chaotique", by Anne Debroise, magasine Science & Vie, February (2017). Interview by Francois Beguin, "Les systèmes physiques échappent-ils aux statistiques ?" Images des Mathématiques, (2017). Traduction in italian in Maddmath. Author of a scientific article described in Un chaos bien plus sauvage qu’escompté ?, Lettre INSMI, 2016 Author of the exhibition "view in 3-manifold" at the 7th European mathematical congress reported in Lettre INSMI, July 2016 Co-author with P.Y. Fave of the exhibition "Um olhar nos espacos de dimensao 3" (Adaptation in Brazil supervised by L. Velho) reported by Valentina Leite, Matemática em três dimensões, brasilian magazine Cienca Hoje, march (2015). Co-author with P.Y. Fave of the exhibition "Um olhar nos espacos de dimensao 3" (Adaptation in Brazil supervised by L. Velho) reported by Cesar Baima, Os espaços do Universo em três dimensões, brasilian jornal O Globo, January the 27th (2015). P. Berger, La théorie du chaos justifie-t-elle un usage constant des statistiques ?, gazette du laga, 2012.