Deformation of geometry and bifurcation of vortex rings

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.Comment: 26 page

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

The relation between local and global dual pairs

In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis (this is well known), while the converse requires a dimension condition (which appears not to be known). We also provide examples illustrating the necessity of the extra conditions

Green infrastructure design for the containment of biological invasions. Insights from a peri-urban case study in Rome, Italy

Secondary shrublands and transitional woodland/shrub formations are recognised to be particularly susceptible to plant invasions, one of the main global threats to biodiversity, especially in dynamic peri-urban landscapes. Urban fringes are in fact often the place for the sprawl of artificial surfaces, fragmentation of habitats, and complex land transitions (including both agriculture intensification and abandonment), which in turn increase propagule pressure of exotic species over residual semi-natural ecosystems. Within this framework, the present study was aimed at analysing i) how landscape composition and configuration affect the richness of woody exotic species in shrubland and transitional woodland/shrub patches, and ii) how this threat can be addressed by means of green infrastructure design in a peri-urban case study (Metropolitan City of Rome, Italy). Accordingly, the occurrence of exotic plants was recorded with field surveys and then integrated with landscape analyses, both at patch level and over a 250&nbsp;m buffer area around each patch. Thus, the effect of landscape features on exotic plant richness was investigated with Generalised Linear Models, and the best model identified (pseudo R-square&nbsp;=&nbsp;0.62) for inferring invasibility of shrublands throughout the study area. Finally, a Green Infrastructure (GI) to contain biological invasion was planned, based on inferred priority sites for intervention and respective, site-tailored, actions. The latter included not only the removal of invasive woody alien plants, but also reforestation and planting of native trees for containment of dispersal and subsequent establishment. Even though specifically developed for the study site, and consistent with local government needs, the proposed approach represents a pilot planning process that might be applied to other peri-urban regions for the combined containment of biological invasions and sustainable development of peripheral complex landscapes

The influence of task demands, verbal ability and executive functions on item and source memory in Autism Spectrum Disorder

Autism Spectrum Disorder (ASD) is generally associated with difficulties in contextual source memory but not single item memory. There are surprising inconsistencies in the literature, however, that the current study seeks to address by examining item and source memory in age and ability matched groups of 22 ASD and 21 comparison adults. Results show that group differences in source memory are moderated by task demands but not by individual differences in verbal ability, executive function or item memory. By contrast, unexpected group differences in item memory could largely be explained by individual differences in source memory. These observations shed light on the factors underlying inconsistent findings in the memory literature in ASD, which has important implications for theory and practice