Utilización de imágenes para introducir conceptos en las clases de ciencias : el caso de la conservación de la energía

La enseñanza de las ciencias, al igual que la propia ciencia, hace uso de diferentes lenguajes: lenguaje verbal, matemático, visual. La creación de significado científico se hace mediante la integración de varios de estos lenguajes. Este tipo de relación entre ellos se suele denominar multimodalidad

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function

New results on averaging theory and applications

Agraïments: The first author is supported by CNPq 248501/2013-5. CAPES grant 88881.030454 /2013-01 from the Program CSF-PVEThe usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e. the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to a non simple zero. Here we provide sufficient conditions in order that the averaging theory can be applied also to non simple zeros for studying their associated periodic solutions. Additionally we do two applications of this new result for studying the zero--Hopf bifurcation in the Lorenz system and in the Fitzhugh--Nagumo system

La cabra mallorquina

Resumen de la comunicación presentada al III Congreso Ibérico sobre Recursos Genéticos Animale