A selection of 10 talks or mini-courses.

1.The closing and connecting lemma in images (Buzios, North East of Rio, November 2003)

Bonatti-Buzios\The Connecting Lemma(s).pdf

 

2.Conference for UMALCA 2004 in Cancun, Mexico.  This is the first conference where I attempt to organize, using conjectures, a program that would allow us to give a general overview of dynamic systems, for the C1 topology.  It was in this conference that I stated for the first time a large number of conjectures.

UMALCA-Cancun-2004.pdf

 

3.Ergodic theory mini-course (Beijing) 2007). Manual notes, edited and typed on a word processor by a student:

Ergodic Theory Minicourse

 

4.Mini-course on robust tangencies, focusing on a result of Moreira (Beijing) August 2009:

·a first part of this course updates, refines and details the program towards a general panorama of dynamic systems, for the C1 topology, outlined at the UMALCA conference in 2004. New conjectures attempt to organize the “wild” dynamics.

· then the course presents examples of robust homoclinic tangencies, then a local process generating such robust tangencies and ensuring the very frequent existence of this dynamic phenomenon, in dimension at least 3

·the main part of this course is dedicated to Moreira's recent result which implies that there are no robust tangencies, in dimension 2, (for the C1 topology).

MinicoursesTangencesRobust

 

5.Panorama of dynamic systems for the C1 topology (Rio September 2009): this is a brief (in 50 minutes) and pictorial version of the program towards a general panorama of dynamic systems presented in the mini-course above.

RioSept2009.pdf

 

 

6. Building Anosov flow: We build Anosov flows as a Lego game by gluing hyperbolic plugs along their boundary components.

Luminy2012.pdf

 

7. Equadiff 2013: I am presenting here a global panorama of Dynamicall System from the point of view of the C1-topology, for a large non-specialised audience.

Equadiff 2013.pdf

 

8. 2016: 7ECM: for the European Conference of Mathematicians, I am presenting the notion of multisingular hyperbolicty: it is a sructure which unifies the hyperbolicity along the regular orbits and the hyperbolicity of the singular points .

7ECM-singular hyperbolicity

 

9. Provo 2017: mini-course on Blenders and applications: robustly transitive dynamics, robust tangencies etc. .

Blenders: provo2017

 

10. Heidelberg 2024: Pseudo-Anosov flows and group actions on the circle

Pseudo-Anosov and group actions on the circle