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 the 2sd 2017, with S. Crovisier (rapporteur interne), F. Ledrappier (rapporteur), M. Lyubich (rapporteur), and with M. Shishikura, D. Turaev, F. Beguin, J. Barral in the jurry.

Article and preprints

P. Berger, Analytic pseudo-rotations, ArXiv, (2022), P. 34.

P. Berger and B. Reinke, Parametric linearization of skew products, ArXiv, (2022), P.24.

P. Berger, N. Gourmelon and M. Helfter, Every diffeomorphism is a total renormalization of a close to identity map, ArXiv, (2022), p.28.

P. Berger and D. Turaev, Generators of groups of Hamitonian maps, to appear in Israel Journal of Math., 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 Sociaty, 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, Inventiones Matematicae, (2016) 205 : 121. 41p. Corrigedum.

P. Berger and R. Dujardin, On stability and hyperbolicty 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-repellor 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).

Proceeding and outreach articles for mathematicans

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, Emergence and para-dynamics, proceeding of the conference in memory to Anosov, 2p. (2016).

Participation to outreach articles and videos

Author of the article Arte multimedia para expresar lo inenarrable de las matemáticas adaptated by Ágata A. Timón, Journal El País, March 22sd (2018).

Author of the exihit recorded in Les noces des mathématiques et des arts by Pierre de Parscau, Journal du CNRS, July (2017).

Author of the exihit Esthetopies recorded in a documentary of 15' by Jean-Baptiste Fave, production IHP, July (2017).

Author of the exihit 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, Jully 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.