An elementary proof of a Lima's theorem for surfaces

An elementary proof of the following theorem is given: THEOREM. Let M be a compact connected surface without boundary. Consider a C∞ action of Rn on M.Then, if the Euler-Poincaré characteristic of M is not zero there exits a fixed point

Smooth actions of connected compact Lie groups with a free point are determined by two vector fields

Consider a smooth action $\mathbf G\times M \rightarrow M$ of a compact connected Lie group $\mathbf G$ on a connected manifold $M$. Assume the existence of a point of $M$ whose isotropy group has a single element (free point). Then we prove that there exist two complete vector field $X,X_1$ such that their group of automorphisms equals $\mathbf G$ regarded as a group of diffeomorphisms of $M$ (the existence of a free point implies that the action of $\mathbf G$ is effective). Moreover, some examples of effective actions with no free point where this result fails are exhibited.Comment: 30 pages, no figures. V2: Major revision. Exposition improved and added a new section presenting some open question

Generalized Lenard Chains, Separation of Variables and Superintegrability

We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte

The ongoing volcanic eruption of El Hierro, Canary Islands

El Hierro, the youngest of the Canary Islands (Spain), is no stranger to hazards associated with volcanic activity or to efforts to minimize the effects of these hazards on local communities. As early as 1793, administrative records of El Hierro indicate that a swarm of earthquakes was felt by locals; fearing a greater volcanic catastrophe, the first evacuation plan of an entire island in the history of the Canaries was prepared. The 1793 eruption was probably submarine with no appreciable consequences other than that the earthquakes were felt [Carracedo, 2008]; over the next roughly 215 years the island was seismically quiet. Yet seismic and volcanic activity are expected on this youngest Canary Island due to its being directly above the presumed location of the Canary Island hot spot, a mantle plume that feeds upwelling magma just under the surface, similar to the Hawaiian Islands. Because of this known geologic activity, the Spanish Instituto Geogrfco Nacional (IGN) has managed geophysical monitoring of the island since the beginning of the 1990s.Peer Reviewe

Los depósitos de ceniza volcánica del Pleistoceno Superior-Holoceno de la región de Tafí del Valle-Cafayate, noroeste de Argentina

[EN]We identified volcanic ash deposits, whose thickness can exceed sometimes the 4 m, in the southeastern margin of La Puna and neighbouring areas (Provinces of Tucuman and Salta, Argentina). These Late Pleistocene and Holocene deposits show the existence of a highly explosive volcanism only some few thousand years ago, without comparison with any historical volcanic episode in northwestern Argentina. We have characterized the size distribution of ash (laser diffraction), morphology of particles (SEM), mineralogy (XRD) and the geochemistry of major and trace elements in bulk sample using mass spectrometry (HR-ICP-MS). The information provided by these deposits is of great interest to size adequately the geochemical impact models of ashfall in future volcanic eruptions in the Central Volcanic Zone of the Andes, quantifying the contribution of volcanic ash to the regional geochemical balances, both with respect to nutrients (e.g., Ca and Fe) and potentially toxic elements (e.g., As and F), among other elements of interest.[ES] Se han localizado diversos depósitos de ceniza volcánica, cuyos espesores llegan a superar en ocasiones los 4 m al suroeste de La Puna y áreas limítrofes (Provincias de Tucumán y Salta, Argentina). Estos depósitos son de edad Pleistoceno Superior y Holoceno y muestran la existencia hace pocos miles de años de volcanismo altamente explosivo, sin comparación con ningún episodio volcánico histórico en el noroeste de Argentina. Se han caracterizado la distribución granulométrica de la ceniza (difracción laser), la morfología de las partículas (microscopía electrónica de barrido), mineralogía (difracción de rayos X) y la geoquímica de elementos mayores y trazas en muestra total mediante espectrometría de masas (HR-ICP-MS). La información suministrada por estos depósitos tiene gran interés a la hora de dimensionar los modelos de impacto geoquímico de la caída de ceniza de futuras erupciones volcánicas en la Zona Volcánica Central de los Andes, cuantificando la contribución de la ceniza volcánica a los balances geoquímicos regionales, tanto por lo que respecta a nutrientes (p. ej., Ca y Fe), como de elementos potencialmente tóxicos (p. ej., As y F), entre otros elementos de interés.Agradecemos el apoyo técnico del labGEOTOP (infraestructura cofinanciada por FEDER, CSIC08-4E-001) del ICTJA-CSIC; de los Grupos PEGEFA (2009-SGR-972) y GEOVOL y fue financiado por el Proyecto QUECA (CGL2011-23307).Peer reviewe

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page

The 2011 submarine volcanic eruption in El Hierro (Canary Islands)

Forty years after the Teneguía Volcano (La Palma, 1971), a submarine eruption took place off the town of La Restinga, south of El Hierro, the smallest and youngest island of the Canarian Archipelago. Precursors allowed an early detection of the event and its approximate location, suggesting it was submarine. Uncertainties derived from insufficient scientific information available to the authorities during the eruption, leading to disproportionate civil protection measures, which had an impact on the island's economy-based primarily on tourism-while residents experienced extra fear and distress. © 2012 Blackwell Publishing Ltd, The Geologists' Association & The Geological Society of London.Peer Reviewe