Tracing KAM tori in presymplectic dynamical systems

We present a KAM theorem for presymplectic dynamical systems. The theorem has a " a posteriori " format. We show that given a Diophantine frequency $\omega$ and a family of presymplectic mappings, if we find an embedded torus which is approximately invariant with rotation $\omega$ such that the torus and the family of mappings satisfy some explicit non-degeneracy condition, then we can find an embedded torus and a value of the parameter close to to the original ones so that the torus is invariant under the map associated to the value of the parameter. Furthermore, we show that the dimension of the parameter space is reduced if we assume that the systems are exact.Comment: 33 pages and one figur

El Canal de Diego Cao y sus depresiones morfológicas (margen del Banco del Guadalquivir, Golfo de Cádiz). Implicaciones oceanográficas y sedimentológicas

The Diego Cao channel is located on the central-north middle slope of the Gulf of Cadiz. It separates the Bartolomeu Dias and Faro sheeted drift plateaus to the north of the Guadalquivir Bank margin uplift. A striking linear series of circular depressions occur parallel to the channel on the Bartolomeu Dias sheeted drift (western channel flank), while a remarkable amphitheater-shaped escarpment affects the channel eastern flank. Their morphological and high- and medium-resolution stratigraphic analysis allows inferring their origin as the result of a complex interplay between oceanographic (bottom currents), mass-wasting and tectonic processes. All features seem to have a common origin, related to an especially active tectonic phase during the Mid-Pleistocene, probably related to adjustments of the deep structural features. Since then, the action of the bottom currents and the local influence of structural processes have shaped the present-day topography. The Diego Cao channel is re-interpreted as a contourite moat associated to a complex mounded, separated drift that includes the circular depressions. They result from contourite deposition over the erosional surface originated by widespread mass-wasting events during the Mid-Pleistocene.Versión del edito

Canonical Melnikov theory for diffeomorphisms

We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or Melnikov displacement can be written in a canonical way. This function is defined to be a section of the normal bundle of the saddle connection. We show how our definition reproduces the classical methods of Poincar\'{e} and Melnikov and specializes to methods previously used for exact symplectic and volume-preserving maps. We use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the Melnikov displacement.Comment: laTeX, 31 pages, 3 figure

The Cadiz Contourite Channel: Sandy contourites, bedforms and dynamic current interaction

The Cadiz Contourite Channel is the largest and most prominent contourite channel in the middle slope of the Gulf of Cadiz, and is known to channelise the southern branch of the Lower Core of Mediterranean Outflow Water (MOW) as it flows westwards from the Gibraltar Gateway. The channel lies in water depth between 650 and 1500 m, is 150 km long, 2–12 km wide, up to 120 m deep, and broadly s-shaped in plan view. It has several associated subparallel marginal channels and shorter spillover channel segments. Its geometry is controlled by the interaction of a strong bottom current with the seafloor morphology, affected by neotectonic deformation and diapiric intrusion. Bottom photographs and dredge hauls reveal a channel floor shaped by high-energy flow, in places with bare rock, boulders and gravel, and elsewhere covered with sandy contourites. The rocky substrate and derived clasts are formed of authigenic iron-rich carbonates, testifying the high degree of fluid escape from adjacent diapiric ridges and mud volcanoes. The sandy substrate shows a wide range of current-induced bedforms including small, straight-crested ripples, large sinuous sand waves and dunes (wavelength 3.5–5 m, height 0.3–0.9 m), weak surface lineation on sands, and aligned gravel stringers and deep erosive scours around large boulders. Bedform orientation indicates flows directed to the south/south-west (main channel) and west (spillover channel), which can be related to MOW bottom currents, and current velocities that vary between about 0.2 and 0.8 m s− 1, even in the same channel location. However, current vane orientation was clearly responding, at least in part, to tidal effects and periodicity in the Gulf of Cadiz at the time the photographs were taken. Maximum current velocities are achieved by a combination of barotropic and internal tides (probably generated at the continental slope) that reinforce the normal MOW flow. In addition, meteorologically-induced internal waves with periods shorter than tidal ones may exert an even greater influence on current intensity, especially when they occur at times of sudden changes of meteorological forcing. This effect further influences MOW variability. In all cases, the funnelling effect of the Cadiz Channel amplifies tidal or meteorologically-induced bottom currents

New alternatives to conventional Internal Medicine

El aumento de la prevalencia de las enfermedades crónicas asociado al envejecimiento de la población es uno de los desafíos más importantes a los que se enfrentan los sistemas de salud en el mundo. Se está produciendo un cambio en los motivos de ingresos hospitalarios, con un alto porcentaje de ellos por motivos diagnósticos mas que terapéuticos, en parte por la presión asistencial a la que se está sometiendo a los dispositivos asistenciales ambulatorios, con generación de importantes listas de espera para estudio

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic

Origin of morphological depressions on the Guadalquivir Bank uplifted area (Gulf of Cadiz middle slope)

We have investigated the origin of morphological depressions (circular-elliptical depressions, amphitheatre-shaped escarpments and valleys) on the Guadalquivir Bank uplifted area (Gulf of Cadiz middle slope). This work is based on swath bathymetry and high- and mid-resolution reflection seismic datasets. Depressions occur on the distal (depositional) sector of the Gulf of Cadiz Contourite Depositional System, which has been developed under the influence of the Mediterranean Outflow Water (MOW). The Guadalquivir Bank is a NE-oriented relief that was uplifted along the Neogene and Quaternary. It forms the southern limit of the Bartolomeu Dias and Faro Sheeted Drift (SD) plateaus that are separated by the NW-trending Diego Cao Contourite Channel. Circular-elliptical depressions occur on the Bartolomeu Dias SD plateau, aligned parallel to the rim of the Diego Cao Channel. Irregular, crescent-shaped depressions occur to the SE of the study area and a valley surrounds the Guadalquivir Bank. The origin of these features is interpreted as the result of the interplay between oceanographic, mass-wasting, tectonic and fluid-escape processes. Four stages define the development of these features: 1) Onset of a contourite mounded drift associated with a proto-Diego Cao moat originated by a weak MOW circulation as it interacted with the structural features of the Guadalquivir Bank during the Lower Pliocene; 2) Evolution to a more complex multi-crest drift and moat system, probably as a result of an enhanced MOW and increased deformation of the underlying structures during the Upper Pliocene-Early Quaternary; 3) Event of enhanced tectonic activity that provoked widespread mass-wasting events along middle slope sheeted drift plateaus during the Mid Pleistocene. It was recorded in a prominent erosive surface under the present-day Diego Cao channel western rim and numerous slide scars displaying amphitheatre shapes on the limits of the plateaus; 4) Final stage (Late Quaternary) when the Mediterranean Intermediate Branch started flowing towards the N-NW along the deep gateway that was opened as a result of the mass-wasting event and/or structural adjustments. The contourite system evolved, due to tectonic events, to the present-day channel and a complex separated drift that includes circular depressions. They result from the interaction between the bottom current and the irregular basal surface created by the slide scars. During this phase, crescent-shaped depressions were created, probably by the interplay between bottom currents and fluid escape processes, and the marginal valley around the Guadalquivir Bank resulted from current reworking of the irregular topography of contouritic deposits affected by slide scars