Research projects

Project CEMAPRE internal

TitleHamiltonian dynamics: new developments beyond integrability
ParticipantsJosé Pedro Gaivão, João Lopes Dias (Principal Investigator)
SummaryThis project addresses the most important questions in Hamiltonian dynamics close to integrable: the
preservation of regular orbits and the onset of chaotic motions. Answering these questions are
essential to understand typical systems, which in turn leads to a better control of its dynamics, in
particular of instabilities that arise naturally in the models.
Since the late 19th century, when the work of Poincaré on Celestial Mechanics opened a major new
field called Dynamical Systems, it was realised that integrable systems are not typical and that
nonlinear terms are at the origin of dynamics very hard to describe.
This awareness created many difficulties in the analysis of problems as diverse as the planetary
motion and the evolution of competing populations. Common to these systems is that they can be
modelled by Hamiltonian differential equations, and are therefore subjected to specific restrictions
that determine their behaviour.