Project CEMAPRE internal
| Title | Hamiltonian dynamics: new developments beyond integrability |
| Participants | José Pedro Gaivão, João Lopes Dias (Principal Investigator) |
| Summary | This 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. |