On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Ra isotopes and Rn as a tool for the water management resources: the Alberquillas aquifer (Málaga-Granada)

The aim of this project is to evaluate the importance of submarine groundwater discharge sector in order to improve the water balance in Málaga-Granada region. The approach of this study arose from the the geology and the aquifers that indicate that there could be some discharge to the sea between Maro (Málaga) and Almuñécar (Granada) and the Andalusian’s Government and its Water Agence were really interested in evaluating it because there is a lot of population and few water available and the magnitude of groundwater discharge has generated controversy. Is well known that water is a scarce resource in this area and it’s very important for the society and for the environment. The legislation, the water policies, the knowledge of the aquifer and the geology, the water dynamics, the land use and the water perception in the society might help the management of this resource not just in Andalusia but in all the Mediterranean basin. The main objective is to evaluate the submarine groundwater discharge from the Alberquillas Aqufier to the sea by measuring 222Rn and Ra isotopes. Specific objectives have been established to achieve the main objective: A) Reveal the importance of water resources in the Mediterranean basin; B) Learn radiometric techniques for the study of groundwater discharge to the sea; C) Learn of sampling techniques of water samples for the measurement of Ra and Rn; D) Learn the techniques for measuring Ra (RaDeCC) and Rn (RAD7); E) Interpretation and discussion of results. During this semester, and in addition of the present study in Málaga- Granada region, the author has participated in the initial phase (sampling, analysis and interpretation of preliminary results) of other research projects focused on the study of submarine groundwater discharges through the use of Ra isotopes and 222Rn. These studies have been developed in different areas, including Alt Empordà (Roses and Sant Pere Pescador), Maresme with CMIMA’s group (Mediterranean Center for Marine and Environmental Research), Delta de l’Ebre, Peñíscola and Mallorca with the IMEDEA’s group (Mediterranean Institute for Advanced Studies).