Adriana da Luz - Singularities and C^1 robustness of dynamical properties
Channel: Centro de Matemática
Date: 2018-11-13

Adriana da Luz  (Universidad de la República) 

Singularities and C^1 robustness of dynamical properties

For diffeomorphisms or for non-singular flows, there are many results relating C^1-robust properties and global structures of the dynamics, as hyperbolicity, partial hyperbolicity, dominated splitting. However, a difficulty appears when a robust property of a flow holds on a set containing recurrent orbits accumulating on a singularity. With Christian Bonatti we propose a general procedure for adapting the usual hyperbolic structures to this context. This allows us to recover to some extent, the relationship between the C^1-robust properties and global structures. In thi talk we show how we can define hyperbolic structures that are compatible with the robust coexistence of singularities and regular orbits in the same chain recurrence class. We discuss the difficulties that make arise from this context that are not present in the context of diffeomorphisms and to what extent does this new definition allows us to overcome them.

Workshop on Groups, Geometry and Dynamics, 23–27 July 2018, Montevideo, Uruguay.

https://ggdworkshop.cmat.edu.uy/

Este vídeo fue filmado y editado por el proyecto OpenFING ( https://open.fing.edu.uy )