Fold-Saddle Bifurcation in Non-Smooth Vector Fields on the Plane

This paper presents results concerning bifurcations of 2D piecewise-smooth dynamical systems governed by vector fields. Generic three parameter families of a class of Non-Smooth Vector Fields are studied and its bifurcation diagrams are exhibited. Our main result describes the unfolding of the so called Fold-Saddle singularity

Slepton mass splittings and cLFV in the SUSY seesaw in the light of recent experimental results

Following recent experimental developments, in this study we re-evaluate if the interplay of high- and low-energy lepton flavour violating observables remains a viable probe to test the high-scale type-I supersymmetric seesaw. Our analysis shows that fully constrained supersymmetric scenarios no longer allow to explore this interplay, since recent LHC data precludes the possibility of having sizeable slepton mass differences for a slepton spectrum sufficiently light to be produced, and in association to BR(mu -> e gamma) within experimental reach. However, relaxing the strict universality of supersymmetric soft-breaking terms, and fully exploring heavy neutrino dynamics, still allows to have slepton mass splittings O(few %), for slepton masses accessible at the LHC, with associated mu -> e gamma rates within future sensitivity. For these scenarios, we illustrate how the correlation between high- and low-energy lepton flavour violating observables allows to probe the high-scale supersymmetric seesaw.Comment: 19 pages, 12 eps figures. References updated; matches version accepted by JHE

Shilnikov problem in Filippov dynamical systems

In this paper we introduce the concept of sliding Shilnikov orbits for $3$D Filippov systems. In short, such an orbit is a piecewise smooth closed curve, composed by Filippov trajectories, which slides on the switching surface and connects a Filippov equilibrium to itself, namely a pseudo saddle-focus. A version of the Shilnikov's Theorem is provided for such systems. Particularly, we show that sliding Shilnikov orbits occur in generic one-parameter families of Filippov systems, and that arbitrarily close to a sliding Shilnikov orbit there exist countably infinitely many sliding periodic orbits. Here, no additional Shilnikov-like assumption is needed in order to get this last result. In addition, we show the existence of sliding Shilnikov orbits in discontinuous piecewise linear differential systems. As far as we know, the examples of Fillippov systems provided in this paper are the first exhibiting such a sliding phenomenon

How Has the Portuguese Innovation Capability Evolved? Estimating a Time Series of the Stock of Technological Knowledge, 1960-2001

The importance of promoting innovation has been elevated up to a status of official standard since the Lisbon European Summit in 2000. Here research and development (R&D) was singled out as an essential element of the foundation on which innovation could be built. R&D has been a growing area of investigation namely at level of firms micro studies aimed at uncovering firms’ innovation capability. At the macro level, the relevance of R&D for countries’ innovation capability has been, in a dynamic perspective, more often presumed rather than effectively tested. This latter limitation is, to a large extent, explained by the paucity of aggregated continuous time series on innovation indicators specifically those based on R&D expenditures. This paper aims at filling this gap by providing an estimate of the Portuguese innovation capability over the two last four decades based on the accumulated R&D efforts. Such indicator, albeit preliminary, will desirably endorse new investigation on the Portuguese catching-up process and, in this way, might inform present and future public programs related to R&D policies in particular and innovation policies in general.Innovation; R&D expenditures; measurement, economic growth