Sylvain Crovisier

Sylvain Crovisier (* 1984 ) is a French mathematician who studies dynamic systems.

Crovisier received his doctorate in 2001 from the University of Paris-South under Jean-Christophe Yoccoz (Nombre de rotation et dynamique faiblement hyperbolique). He is Research Director of the CNRS at the University of Paris-South.

In 2009, together with Christian Bonatti and Amie Wilkinson , he solved the centralizer problem for diffeomorphisms in the case. The problem was one of Stephen Smale's list of 18 open problems ( Smale Problems , 1998). Recently, together with Artur Ávila and Amie Wilkinson, he proved that generic volume-preserving diffeomorphisms with positive metric entropy form an ergodic- dynamic system ( this does not apply to Hamiltonian systems according to Kolmogorow, Arnold and Moser ). ${\ displaystyle C ^ {1}}$ ${\ displaystyle C ^ {1}}$ ${\ displaystyle C ^ {\ infty}}$

In 2014 he was invited speaker at the International Congress of Mathematicians in Seoul (Dynamics of -diffeomorphisms: global description and prospects for classification Zeta functions for Anosov flows). ${\ displaystyle C ^ {1}}$

Fonts

with M.-C. Arnaud, C. Bonatti: Dynamiques symplectiques génériques. Ergodic Theory Dynam. Systems 25 (2005), 1401-1436.

with Abdenur, Bonatti, Diaz, Wen: Periodic points and homoclinic classes. Ergodic Theory Dynam. Systems 26: 1-22 (2006).

with Abdenur, Bonatti, Diaz: Generic diffeomorphisms on compact surfaces. Fundamenta Mathematicae 187 (2005), 127-159.

with bonatti : Récurrence et généricité. Invent. Math. 158 (2004), 33-104.

with Martin Sambarino, Dawei Yang: Partial Hyperbolicity and Homoclinic Tangencies , Journal of the European Mathematical Society 17 (2015), 1-49, Arxiv 2011

Perturbation de la dynamique de difféomorphismes en petite régularité, Astérisque, volume 354, 2013

with Enrique Pujals : Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon / mechanism for diffeomorphisms, Inventiones Mathematicae, Volume 201, 2015, pp. 385-517.

Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems, Annals of Mathematics, Volume 172, 2010, pp. 1641–1677.

with C. Bonatti, A. Wilkinson: The C1-generic diffeomorphism has trivial centralizer, Publ. Math. IHES., Volume 109, 2009, pp. 185-244.

with Artur Avila, Amie Wilkinson: Diffeomorphisms with positive metric entropy, Arxiv 2014

Web links

Homepage

Individual evidence

↑ Sylvain Crovisier in the Mathematics Genealogy Project (English)
↑ C. Bonatti, S. Crovisier, A. Wilkinson The C1-generic diffeomorphism has trivial centralizer , Publications Mathématiques de l'IHÉS, 109, 2009, 185–244

personal data
SURNAME	Crovisier, Sylvain
BRIEF DESCRIPTION	French mathematician
DATE OF BIRTH	1984

[1] Sylvain Crovisier in the Mathematics Genealogy Project (English)

[2] C. Bonatti, S. Crovisier, A. Wilkinson The C1-generic diffeomorphism has trivial centralizer , Publications Mathématiques de l'IHÉS, 109, 2009, 185–244