## Project CEMAPRE internal

Title | Gevrey renormalization of vector fields on the torus |

Participants | José Pedro Gaivão, João Lopes Dias (Principal Investigator) |

Summary | Quasi-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. |