Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Multiple maps and activity-dependent representational plasticity in the anterior Wulst of the adult barn owl (Tyto alba)

In the present study we addressed the issue of somatosensory representation and plasticity in a nonmammalian species, the barn owl. Multiunit mapping techniques were used to examine the representation of the specialized receptor surface of the claw in the anterior Wulst. We found dual somatotopic mirror image representations of the skin surface of the contralateral claw. In addition, we examined both representations 2 weeks after denervation of the distal skin surface of a single digit. In both representations, the denervated digital representation became responsive to stimulation of the adjacent, mutually functional, digit. The mutability and multiple representations indicates that the Wulst provides the owl with sensory processing capabilities analogous to those in mammals.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.

Pagamento de proventos versus preços deações maduras e em expansão segundo Kohonen Maps

Este estudo investiga se a política de distribuição de resultados seria capaz de alterar os preços das ações de uma empresa. O objetivo deste trabalho é discutir os impactos do pagamento de proventos sobre os preços das ações, na data ex direito, de empresas maduras e de empresas em expansão, considerando-se ainda o efeito da classe da ação (ordinária ou preferencial) sobre os resultados. Para tal, adotou-se a metodologia de dados em painel, segmentando a amostra a partir dos Mapas Auto-organizáveis de Kohonen. Os resultados revelam que a estratégia de curto prazo de comprar ações na última data com, vender na primeira data ex e embolsar os dividendos é capaz de gerar perdas de capital que superam em até quatro vezes o ganho líquido decorrente do provento embolsado.

Tsunami vulnerability assessment of Casablanca-Morocco using numerical modelling and GIS tools

Earthquakes and tsunamis along Morocco's coasts have been reported since historical times. The threat posed by tsunamis must be included in coastal risk studies. This study focuses on the tsunami impact and vulnerability assessment of the Casablanca harbour and surrounding area using a combination of tsunami inundation numerical modelling, field survey data and geographic information system. The tsunami scenario used here is compatible with the 1755 Lisbon event that we considered to be the worst case tsunami scenario. Hydrodynamic modelling was performed with an adapted version of the Cornell Multigrid Coupled Tsunami Model from Cornell University. The simulation covers the eastern domain of the Azores-Gibraltar fracture zone corresponding to the largest tsunamigenic area in the North Atlantic. The proposed vulnerability model attempts to provide an insight into the tsunami vulnerability of building stock. Results in the form of a vulnerability map will be useful for decision makers and local authorities in preventing the community resiliency for tsunami hazards.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Paleomagnetic study of the Great Foum Zguid dyke (southern Morocco): A positive contact test related to metasomatic processes

When a paleomagnetic pole is sought for in an igneous body, the host rocks should be subjected to a contact test to assure that the determined paleopole has the age of the intrusion. If the contact test is positive, it precludes the possibility that the measured magnetization is a later effect. Therefore, we investigated the variations of the remanent magnetization along cross-sections of rocks hosting the Foum Zguid dyke (southern Morocco) and the dyke itself. A positive contact test was obtained, but it is mainly related with Chemical/Crystalline Remanent Magnetization due to metasomatic processes in the host-rocks during magma intrusion and cooling, and not only with Thermo-Remanent Magnetization as ordinarily assumed in standard studies. Paleomagnetic data obtained within the dyke then reflect the Earth magnetic field during emplacement of this well-dated (196.9 +/- 1.8 Ma) intrusion.

Preliminary results of a study of magnetic properties in the Foum-Zguid dyke (Morocco)

This work focuses on the study of flow and propagation of magma using rock magnetic analyses along sections across the thick Jurassic dyke of Foum-Zguid (Southern Morocco). Thermomagnetic data show that Ti-poor titanomagnetite is the main magnetic carrier. Petrographic analysis shows that the main Ti phase (ilmenite) occurs either as lamellae within spinel (center of the dyke) or as isolated grains (dyke margin). Bulk magnetic properties display distinct behavior according to the distance to the dyke margin; grain size of the main magnetic carrier decreases towards the center of the dyke, while the natural remanent magnetization and the bulk magnetic susceptibility increase. Only the magnetic susceptibility ellipsoid close to the dyke margin corresponds to that usually found in thin dykes, with the magnetic foliation sub parallel to dyke margins. Maximum principal axis is in most cases either parallel or perpendicular to the intersection between the planes of magnetic foliation and dyke wall. Moreover, when this axis is perpendicular to the intersection it is associated with a more oblate magnetic susceptibility ellipsoid shape, indicating the presence of complex magnetic fabrics. The studied magnetic properties show that, in this 100 m wide thick dyke, flow structures related with dyke propagation are only preserved close to the quickly cooled dyke margins.

Thick dyke emplacement and internal flow: A structural and magnetic fabric study of the deep-seated dolerite dyke of Foum Zguid (southern Morocco)

Knowledge on forced magma injection and magma flow in dykes is crucial for the understanding of how magmas migrate through the crust to the Earth's surface. Because many questions still persist, we used the long, thick, and deep-seated Foum Zguid dyke (Morocco) to investigate dyke emplacement and internal flow by means of magnetic methods, structural analysis, petrography, and scanning electron microscopy. We also investigated how the host rocks accommodated the intrusion. Regarding internal flow: 1. Important variations of the rock magnetic properties and magnetic fabric occur with distance from dyke wall; 2. anisotropy of anhysteretic remanent magnetization reveals that anisotropy of magnetic susceptibility (AMS) results mainly from the superposition of subfabrics with distinct coercivities and that the imbrication between magnetic foliation and dyke plane is more reliable to deduce flow than the orientation of the AMS maximum principal axis; and 3. a dominant upward flow near the margins can be inferred. The magnetic fabric closest to the dyke wall likely records magma flow best due to fast cooling, whereas in the core the magnetic properties have been affected by high-temperature exsolution and metasomatic effects due to slow cooling. Regarding dyke emplacement, this study shows that the thick forceful intrusion induced deformation by homogeneous flattening and/or folding of the host sedimentary strata. Dewatering related to heat, as recorded by thick quartz veins bordering the dyke in some localities, may have also helped accommodating dyke intrusion. The spatial arrangement of quartz veins and their geometrical relationship with the dyke indicate a preintrusive to synintrusive sinistral component of strike slip.

Variation of magnetic properties in sedimentary rocks hosting the Foum Zguid dyke (southern Morocco): Combined effects of re-crystallization and Fe-metasomatism

The effects of dyke intrusion on the magnetic properties of host sedimentary rocks are still poorly understood. Therefore, we have evaluated bulk magnetic parameters of standard palaeomagnetic samples collected along several sections across the sediments hosting the Foum Zguid dyke in southern Morocco. The study has been completed with the evaluation of the magnetic fabric after laboratory application of sequential heating experiments. The present study shows that: (1) close to Fourn Zguid dykes, the variations of the bulk magnetic parameters and of the magnetic fabric is strongly related with re-crystallization and Fe-metasomatism intensity. (2) The thermal experiments on AMS of samples collected farther from the dyke and, thus, less affected by heating during dyke emplacement, indicate that 300-400 degrees C is the minimum experimental temperature necessary to trigger appreciable transformations of the pre-existing magnetic fabrics. For temperatures higher than ca. 580 degrees C, the magnetic fabric transformations are fully realized, with complete transposition of the initial fabric to a fabric similar to that of samples collected close to the dyke. Therefore, measured variations of the magnetic fabric can be used to evaluate re-crystallization temperatures experienced by the host sedimentary rock during dyke emplacement. The distinct magnetic behaviour observed along the cross-sections strongly suggests that samples collected farther from the dyke margins did not experience thermal episodes with temperatures higher than 300 degrees C after dyke emplacement. (3) AMS data shows a gradual variation of the magnetic fabric with distance from the dyke margin, from sub-horizontal K-3 away from the dyke to vertical K3 close to the dyke. Experimental heating shows that heat alone can be responsible for this strong variation. Therefore, such orientation changes should not be unequivocally interpreted as the result of a stress field (resulting from the emplacement of the dyke, for instance). (4) Magnetic studies prove to be a very sensitive tool to assess rock magnetic transformations, thermally and chemically induced by dyke intrusion in hosting sediments.

In permanent transit: discourses and maps of the intercultural experience

Instituto Politécnico do Porto. Instituto Superior de Contabilidade e Administração do Porto

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.