Research projects

Project CEMAPRE internal

TitlePersistence of homoclinic tangencies near saddle-centre bifurcations
ParticipantsPedro Duarte, José Pedro Gaivão (Principal Investigator)
SummaryThe 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.