Research projects

Project CEMAPRE internal

TitleGevrey renormalization of vector fields on the torus
ParticipantsJosé Pedro Gaivão, João Lopes Dias (Principal Investigator)
SummaryQuasi-periodic discrete-time dynamics is a regular motion that corresponds to the rotation by an
irrational angle on the circle with perimeter equal to one. This is almost a periodic orbit since it
returns arbitrarily close to the initial point and it does not have dependence on the initial
conditions (thus it is not a chaotic orbit). It is a known fact that any real-analytic
diffeomorphism sufficiently close to a rotation on the circle is equivalent to a rotation if the
rotation number is of Brjuno-type (an arithmetic condition related to the continued fractions
expansion). There is the equivalent version for flows on the torus. We want to show that this
phenomena still holds in the context of Gevrey vector fields for a new Brjuno-type condition on
rotation vectors which strictly contains all diophantine vectors.