Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Oxygen isotope thermometry in carbonatites, Fuerteventura, Canary Islands, Spain

Crystallization temperatures of the oceanic carbonatites of Fuerteventura, Canary Islands, have been determined from oxygen isotope fractionations between calcite, silicate minerals (feldspar, pyroxene, biotite, and zircon) and magnetite. The measured fractionations have been interpreted in the light of late stage interactions with meteoric and/or magmatic water. Cathodoluminescence characteristics were investigated for the carbonatite minerals in order to determine the extent of alteration and to select unaltered samples. Oxygen isotope fractionations of minerals of unaltered samples yield crystallization temperatures between 450 and 960degreesC (average 710degreesC). The highest temperature is obtained from pyroxene-calcite pairs. The above range is in agreement with other carbonatite thermometric Studies. This is the first study that provides oxygen isotope data coupled with a CL study on carbonatite-related zircon. The CL pictures revealed that the zircon is broken and altered in the carbonatites and in associated syenites. Regarding geological field evidences of syenite-carbonatite relationship and the close agreement of published zircon U/Pb and whole rock and biotite K/Ar and Ar-Ar age data, the most probable process is early zircon crystallization from the syenite magma and late-stage reworking during magma evolution and carbonatite segregation. The oxygen isotope fractionations between zircon and other carbonatite minerals (calcite and pyroxene) support the assumption that the zircon would correspond to the early crystallization of syenite-carbonatite magmas.

The tectonically controlled emplacement of a vertically sheeted gabbro-pyroxenite intrusion: Feeder-zone of an ocean-island volcano (Fuerteventura, Canary Islands)

The Miocene PX1 gabbro-pyroxenite pluton, Fuerteventura, Canary Islands, is a 3.5 x 5.5 km shallow-level intrusion (0.15-0.2 GPa and 1100-1120 degrees C), interpreted as the feeder-zone to an ocean-island volcano. It displays a vertical magmatic banding expressed in five 50 to 100 metre-wide NNE-SSW trending alkaline gabbro sequences alternating with pyroxenites. This emplacement geometry was controlled by brittle to ductile shear zones, generated by a regional E-W extensional tectonic setting that affected Fuerteventura during the Miocene. At a smaller scale, the PX1 gabbro and pyroxenite bands consist of metre-thick differentiation units, which suggest emplacement by periodic injection of magma pulses as vertical dykes that amalgamated, similarly to a sub-volcanic sheeted dyke complex. Individual dykes underwent internal differentiation following a solidification front parallel to the dyke edges. This solidification front may have been favoured by a significant lateral/horizontal thermal gradient, expressed by the vertical banding in the gabbros, the fractionation asymmetry within individual dykes and the migmatisation of the wall rocks. Pyroxenitic layers result from the fractionation and accumulation of clinopyroxene +/- olivine +/- plagioclase crystals from a mildly alkaline basaltic liquid. They are interpreted as truncated differentiation sequences, from which residual melts were extracted at various stages of their chemical evolution by subsequent dyke intrusions, either next to or within the crystallising unit. Compaction and squeezing of the crystal mush is ascribed to the incoming and inflating magma pulses. The expelled interstitial liquid was likely collected and erupted along with the magma flowing through the newly injected dykes. Clinopyroxene mineral orientation - as evidenced by EBSD and micro X-ray tomography investigations - displays a marked pure-shear component, supporting the interpretation of the role of compaction in the generation of the pyroxenites. Conversely, gabbro sequences underwent minor melt extraction and are believed to represent crystallised coalesced magma batches emplaced at lower rates at the end of eruptive cycles. Clinopyroxene orientations in gabbros record a simple shear component suggesting syn-magmatic deformation parallel to observed NNE-SSW trending shear zones induced by the regional tensional stress field. This emplacement model implies a crystallisation time of 1 to 5 years for individual dykes, consistent with PX1 emplacement over less than 0.5 My. A minimum amount of approximately 150 km(3) of magma is needed to generate the pluton, part of it having been erupted through the Central Volcanic Centre of Fuerteventura. If the regional extensional tectonic regime controls the PX1 feeder-zone initiation and overall geometry, rates and volumes of magma depend on other, source-related factors. High injection rates are likely to induce intrusion growth rates larger than could be accommodated by the regional extension. In this case, dyke intrusion by propagation of a weak tip, combined with the inability of magma to circulate through previously emplaced and crystallised dykes could result in an increase of non-lithostatic pressure on previously emplaced mushy dyke walls; thus generating strong pure-shear compaction within the pluton feeder-zone and interstitial melt expulsion. These compaction-dominated processes are recorded by the cumulitic pyroxenite bands. (C) 2010 Elsevier B.V. All rights reserved.

Epidemiology and prevention of cardiovascular disease in the Seychelles Islands (Indian Ocean)

This article presents selected findings and lessons from a cardiovascular research and prevention program initiated in 1989 in the Republic of Seychelles, a country in demographic and epidemiological transition. Rapid and sustained aging of the population (e.g., two-fold increase of people aged 30-39 from 1979 to 1995) implies, over the next few decades, further dramatic increase of the burden of chronic diseases, particularly cardiovascular disease (CVD). Epidemiological surveillance shows high age-specific rates of CVD (particularly stroke), high prevalence of peripheral atherosclerosis (plaques in carotid and femoral arteries), high prevalence of classical modifiable risk factors in the adult population (particularly hypertension), and substantial proportions of children with overweight. Stagnant life expectancy in men and an increase in women have been observed over the last two decades; this occurred despite largely improved health services and reduced infant mortality rates, and may reflect the large CVD burden found in middle-aged men (less so in middle-aged women). A national program of prevention of CVD has been initiated since 1991, which includes a mix of interventions to reduce risk factors in the general population and in high-risk individuals. Substantial research to back the prevention program indeed shows, at the moment, epidemiological patterns in Seychelles similar to those observed in Western countries (e.g., an association between peripheral atherosclerosis [as a proxy of CVD] and low density lipoprotein-cholesterol, smoking, diabetes, and [inversely] walking). This clearly supports the view that promotion of healthy lifestyles and control of conventional risk factors should be the main targets for CVD prevention and control.

Shallow-level migmatization of gabbros in a metamorphic contact aureole, Fuerteventura Basal Complex, Canary Islands

Migmatization of gabbroic rocks at 2-3 kbar has occurred in the metamorphic contact aureole of a mafic pluton in the Fuerteventura Basal Complex (Canary Island;). Migmatites are characterized by a dense network: of closely spaced millimetre-wide leucocratic veins with perfectly preserved igneous textures. They are all relatively enriched in Al, Na I: Sr Ba, Nb, Y and the rare earth elements compared with the unaffected country rock beyond the aureole. Migmatization under such low-pressure conditions war possible because of the unusual tectonic and magmatic contact in which ii occurred. Multiple basic intrusions associated with extrusive volcanic activity created high heat flow in a small area. Alkaline and metasomatized rocks present in the country rock of the intruding pluton were leached by high-temperature fluids during contact metamorphism. These enriched fluids then favoured partial melting of the host gabbroic rocks, and contaminated both the leucosomes and melanosomes. A transpressive tectonic setting at the time of intrusion created shearing along the contact between the intrusion and its host rock. This shearing enhanced circulation of the fluids and allowed segregation of the nea-formed melts from their restite by opening tension veins into which the melts migrated. Depending on the relative timing of melt segregation and recrystallization leucosomes range in composition from a 40-60% mixture of clinopyroxene (+/- amphibole) and plagioclase to almost pure feldspathic veins. Comparable occurrences of gabbros migmatized at low pressure are expected only at a snail scale in localized areas of high heat flow in the presence of fluids, such as in. mid-ocean ridges or ocean-islands.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Quasiconformal maps, analytic capacity, and non linear potentials

"Vegeu el resum a l'inici del document del fitxer adjunt."

Threats from climate change to terrestrial vertebrate hotspots in europe.

We identified hotspots of terrestrial vertebrate species diversity in Europe and adjacent islands. Moreover, we assessed the extent to which by the end of the 21(st) century such hotspots will be exposed to average monthly temperature and precipitation patterns which can be regarded as extreme if compared to the climate experienced during 1950-2000. In particular, we considered the entire European sub-continent plus Turkey and a total of 1149 species of terrestrial vertebrates. For each species, we developed species-specific expert-based distribution models (validated against field data) which we used to calculate species richness maps for mammals, breeding birds, amphibians, and reptiles. Considering four global circulation model outputs and three emission scenarios, we generated an index of risk of exposure to extreme climates, and we used a bivariate local Moran's I to identify the areas with a significant association between hotspots of diversity and high risk of exposure to extreme climates. Our results outline that the Mediterranean basin represents both an important hotspot for biodiversity and especially for threatened species for all taxa. In particular, the Iberian and Italian peninsulas host particularly high species richness as measured over all groups, while the eastern Mediterranean basin is particularly rich in amphibians and reptiles; the islands (both Macaronesian and Mediterranean) host the highest richness of threatened species for all taxa occurs. Our results suggest that the main hotspots of biodiversity for terrestrial vertebrates may be extensively influenced by the climate change projected to occur over the coming decades, especially in the Mediterranean bioregion, posing serious concerns for biodiversity conservation.

Aplicación con Google Maps

El principal objetivo de este proyecto es realizar un aplicativo web que utilice API’s para que, a partir de un conjunto de rutas almacenadas en el sistema, éste sea capaz de generar nuevas rutas a partir de éstas, de modo que dicho sistema no se comporte como un mero "almacén" de rutas introducidas por los usuarios para poder ser utilizadas por los demás posteriormente, sino que podamos ser nosotros mismos los que decidamos ciertos aspectos de la ruta que deseamos que el sistema nos proporcione. Así, el aplicativo desarrollado, partiendo de un conjunto previo de rutas, será capaz de generar nuevas rutas pasando lo más cerca posible de un conjunto de puntos definidos por el usuario, pudiendo ser calculadas siguiendo diferentes parámetros de optimización tales como el menor número de rutas utilizadas en el cálculo o el menor número de intersecciones entre ellas. Estas rutas, posteriormente, pueden visualizarse en la aplicación mediante el API de Google Maps, o pueden ser descargadas para utilizarlas en nuestro dispositivo GPS portátil.

Geolocalitzáció en temps real sobre Google Maps

L’objectiu d’aquest projecte és crear un sistema de seguiment d’una flota de vehicles amb GPS en temps real. A partir d’un mòdul de captació, el servidor recull la informació geogràfica dels vehicles i l’emmagatzema. I amb un mòdul de processament, es mostra i controla els vehicles, els punts d’interès i els polígons del sistema de Geofencing. En primer lloc, faig una introducció a l’estat de l’art dels sistemes de seguiment de vehicles. A continuació, analitzo els requeriments, especifico el comportament desitjat del sistema, explico el disseny i la implementació. Per últim, faig un seguit de proves per extreure’n les conclusions.

Spatial distribution of economic activities: an empirical approach usingself-organizing maps

The aim of this paper is to analyse the colocation patterns of industries and firms. We study the spatial distribution of firms from different industries at a microgeographic level and from this identify the main reasons for this locational behaviour. The empirical application uses data from Mercantile Registers of Spanish firms (manufacturers and services). Inter-sectorial linkages are shown using self-organizing maps. Key words: clusters, microgeographic data, self-organizing maps, firm location JEL classification: R10, R12, R34