0000000000144639
AUTHOR
Carlos Gutierrez
Plane foliations with a saddle singularity
Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.
Trypanosoma evansi infection in mainland Spain.
An outbreak of Trypanosoma evansi infection that occurred in mainland Spain is described. The outbreak occurred on an equine and camel farm to which dromedary camels from an infected area of the Canary Islands had recently been introduced. One of these camels developed clinical signs and T. evansi was discovered in a blood smear examination. The herd was evaluated in order to determine the extent of the disease. The results showed that 76% of the camels, 35% of the donkeys and 2% of the horses were affected. The animals were isolated and treated using Cymelarsan((R)) (0.5mg/kg). After treatment, three blood analysis using parasitological methods revealed negative results. This is the first …
Hopf bifurcation at infinity for planar vector fields
We study, from a new point of view, families of planar vector fields without singularities $ \{ X_{\mu}$  :  $-\varepsilon < \mu < \varepsilon\} $ defined on the complement of an open ball centered at the origin such that, at $\mu=0$, infinity changes from repellor to attractor, or vice versa. We also study a sort of local stability of some $C^1$ planar vector fields around infinity.
Morphological and biometrical features of Trypanosoma evansi isolates from an outbreak in mainland Spain.
According to several authors, Trypanosoma evansi is a monomorphic trypanosome found exclusively in slender intermediate forms, although additional studies have revealed that many strains present stumpy forms on rare occasions. In a recent T. evansi outbreak in mainland Spain, several atypical forms were observed in blood smear examinations. Molecular procedures were then necessary to confirm the causal agent. Morphological and biometric measures were taken to characterize the different forms of T. evansi. In contrast to published information, the results of this study would indicate that biometrically distinct T. evansi could also be found in the same farm and even in the same animal specie…
Planar maps whose second iterate has a unique fixed point
Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) t…