Research projects

Project CEMAPRE internal

TitleGeneric properties of $C^2$ Hamiltonians
ParticipantsJoão Lopes Dias (Principal Investigator), Filipe Santos
SummaryA major result in the generic theory of smooth dynamical systems was recently obtained by Bochi,
following some ideas by Mane. It says that a $C^1$-generic symplectomorphism on a compact manifold
is either partially hyperbolic or else it has zero Lyapunov exponents almost everywhere. This
reduces (in the $C^1$-topology) the multitude of dynamics of a generic system. In particular,
non-uniformly hyperbolic systems (with positive Lyapunov exponents but not partially hyperbolic) are
not generic. We deal with the version of this result for Hamiltonian flows.