Project CEMAPRE internal
| Title | Geometric renormalization of area-preserving twist maps |
| Participants | João Lopes Dias (Principal Investigator) |
| Summary | The widely-known Kolmogorov-Arnold-Moser (KAM) results have been around for more than 50 years. They relate stability of dynamic behaviour with the arithmetic properties of numbers and vectors. This surprising fact is of a very subtle nature, and it marked a great breakthrough in the understanding of the dynamics of conservative systems. The original method of proof due to Kolmogorov was based in an adaptation of the Newton method. A recent new approach deals with a different approach, with consists on the rescaling of phase space and the re-parametrisation of time. This is known as renormalisation. Our goal is to use renormalisation techniques in order to improve results first obtained by KAM methods. |