Research projects

Project CEMAPRE internal

TitleAlmost linearization of irrational toroidal flows
ParticipantsJosé Pedro Gaivão, João Lopes Dias (Principal Investigator)
SummaryIrrational flows on the torus are generated by vector fields with a unique rotation vector that is
rationally independent. In dimension two, by taking the return map to a section of the flow, they
correspond to circle diffeomorphisms with irrational rotation number. Under conditions, they are
linearizable in the sense that in some coordinates the flow is a straight line with irrational
direction. So, they are minimal, i.e. all orbits are dense in the torus. More general notions are
notoriously important for applications, namely the almost linearization. In this case, one can turn
the flow arbitrarily close to a straight line. It is expected that this holds for much more general