## DYNAMICAL SYSTEMS Seminar

### Robust cycles (homoclinic tangencies and heterodimensional cycles)

Lorenzo Diaz
(PUC - Rio)

Abstract: We discuss the generation of robust cycles for $C^1$-diffeomorphisms. We first prove that heterodimensional cycles (i.e., cycles associated to saddles having different indices -dimension of the unstable bundle) yield robust cycles (associated to non-trivial hyperbolic sets with different indices). Finally, we state sufficient conditions for the generation of robust homoclinic tangencies, i.e., non-transverse intersections between the invariant (stable and unstable) manifolds of hyperbolic sets. These conditions are related to the weak hyperbolicity (domination) of the system.

Tuesday, February 9, 2010
Time: 16h30
Room: B1-01, Complexo Interdisciplinar, UL
http://cemapre.iseg.ulisboa.pt/seminars/dynsys/