Hyperbolic interweaving in dynamics

05.09.2021 - 10.09.2021 | Online

     Hyperbolic Interwaiving in Dynamics                                                        Celebrating Lorenzo J. Díaz 60th birthday                                                         September 06 - 08,  2021                                                                                                                                                                                         

Hyperbolic interweaving in dynamics
    Amie Wilkinson (University of Chicago)  
    Anton Gorodetski (University of California  Irvine)  
    Carlangelo Liverani (University of Roma Tor Vergata)  
    Carlos Vasquez (Pontifical Catholic University of Valparaiso)  
    Christian Bonatti (Université de Bourgogne)  
    Fabio Tal (University of São Paulo)   
    Federico R. Hertz (Penn State University)  
    Katrin Gelfert (Federal University of Rio de Janeiro)        
    Omri Sarig (The Weizmann Inst. Sc.)  
    Sebastian van Strien (Imperial College)  
    Shin Kiriki (Tokai University)
    Sylvain Crovisier (University Paris-Sud XI)

The conference will be in honor of Professor Lorenzo J. Díaz on the occasion of his 60 birthday. Díaz is a renowned expert in dynamical systems, with an impressive list of research papers, many of which in major mathematical journals. 
He was an invited speaker at the ICM2018. 
He is perhaps the world's leading figure in the theory of heterodimensional cycles. His doctoral thesis already contained the germ of the notion of a “blender” that he later developed jointly with C. Bonatti, and which proved to be a key model for understanding robust transitivity and robust non-hyperbolicity of high dimensional maps from the topological and ergodic points of view.
Indeed, he played a pivotal role in the characterization of robustly transitive diffeomorphisms.
In a different direction, he constructed the first examples of prevalent global strange attractors 
dealing with so-called critical saddle-node cycles. Díaz has also been leading the effort to characterize C^1-generic dynamics, especially in high dimensions. Among his main contributions in this direction, one must highlight the construction of several models of “wild” dynamics. Over the last decade, Díaz has also been most interested in the study of (persistent) non-hyperbolic invariant ergodic measures, that is, having zero as a Lyapunov exponent. Currently, he is studying, mainly in collaboration with Michal Rams (IM PAN) and Katrin Gelfert (UFRJ, Brasil), thermodynamical aspects of partially hyperbolic systems.

The topics of the conference will encompass this wide but nevertheless intertwined spectrum of fields. 
The already classical book by Christian Bonatti, Lorenzo Diaz and Marcelo Viana “Dynamics Beyond Hyperbolicity: A global Geometric and Probabilistic Perspective” must be invoked. 
The area derives from Poincare, later S. Smale, D. Anosov, Ya. Sinai, J. Palis, J.-Ch. Yoccoz, A. Katok.
It has vibrant centers in Brasil, France, England, China, USA, and other countries.


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