2023.12.7 14.30 Room 233B of the International Center of Mathematics Speaker: Carlos Gustavo Moreira.

Title: On the denseness of finitude of sinks

Abstract: In 1995, Jacob Palis stated an ambitious conjecture on denseness of finitude of attractors for diffeomorphisms in arbitrary dimensions. Before that, Newhouse proved the existence of residual sets of  surface diffeomorphisms (in certain nonempty open sets) in the C² topology displaying infinitely many sinks (hyperbolic periodic attractors), and Bonatti and Diaz did the same in the C¹ topology in higher dimensions. 

We will discuss the problem of proving the denseness (in the C¹ topology) of diffeomorphisms (in arbitrary dimensions) displaying only a finite number of sinks. This is a joint work with Fernando Lenarduzzi and Jacob Palis.