1. Dynamics of fluids and populations
We plan to study in particular the stability of natural phenomena of particular interest as meteorological ones (typhoon, atmospherical convection, ect...), glaciers and ecological systems. We also plan to extend our research to stochastic perturbations.

2. Dynamics of planar systems
We shall study the existence of suitable normalizers, that could allow to estimate the sign of the first and/or second derivative of the period function. This should lead to give sufficient conditions for the monotonicity and/or the convexity of the period, in relation to suitable hypotheses on the considered vector field. Such results will be applied to differential equations appearing in the study of mechanical or electric systems.

3. Nonholonomic dynamics
First of all we plan to deepen the theory given in the paper Furta, Zampieri: "Cruising in a central force field", Portug. Mathem., vol. 61 (2004), pp. 259-280, characterizing all central potential
which have all cruise orbits periodic. To this extent some ideas introduced in Zapieri: "Liapunov stability for some central forces", J. Diff. Eq., vol. 74 (1988), pp. 254-265, will be used. This research is a joint work with G. Gorni of the Udine section of the project and with G. De Marco of Padova University.

4. Global stability
We will look for a counterexemple to Markus Yamabe conjecture among Lotka-Volterra systems, proposed by Hofbauer and Sigmund. We plan to use techniques of partial compactification.