Research projects

Project CEMAPRE internal

TitleSplitting of separatrices near resonant elliptic fixed points of area preserving maps
ParticipantsJosé Pedro Gaivão (Principal Investigator)
SummaryThe standard method to detect the splitting of separatrices is the Poincar-Melnikov-Arnold (PMA)
method. In singular analytic perturbation theory the splitting of separatrices is often
exponentially small when compared to the perturbation parameter and the PMA method does not give a
correct answer. Measuring the splitting is crucial to obtain an estimate on the size of the chaotic
region. An important problem with this feature is to obtain an asymptotic expansion measuring the
splitting of separatrices near resonant elliptic fixed points of area preserving maps.