Research projects

Project CEMAPRE internal

TitleGeometric renormalization of area-preserving twist maps
ParticipantsJoão Lopes Dias (Principal Investigator)
SummaryThe 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.