Research projects

Project CEMAPRE internal

 Title Persistence of homoclinic tangencies near saddle-centre bifurcations Participants Pedro Duarte, José Pedro Gaivão (Principal Investigator) Summary The abundance of wild hyperbolic sets and the coexistence of infinitely many elliptic points is widely known as Newhouse phenomenon. A mechanism for the creation of such phenomenon is the generic unfolding of a homoclinic tangency. There are open sets of maps exhibiting persistence of homoclinic tangencies. However, few results are known for parametric families, since it involves studying the exponentially small splitting of separatrices which is a hard problem. In this project we will study the persistence of homoclinic tangencies near saddle-centre bifurcations.