The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps

We probe deeper into the Discrete Markus-Yamabe Question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an affirmative answer to the Discrete Markus-Yamabe Question are those possessing Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map

Global Saddles for Planar Maps

We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of $D_2$-symmetric maps, for which we obtain a similar result for $C^1$ homeomorphisms. Some applications to differential equations are also given

Preventive health services for systemic lupus erythematosus patients: whose job is it?

Apropos of the article about preventive health care for patients with systemic lupus erythematosus in this issue of Arthritis Research & Therapy, we offer some thoughts about how best to delineate the roles of the specialist (rheumatologist) and the generalist in the provision of services to these patients. Even in the best circumstances, these services are now provided at a rate that is less than optimal. We also offer a point about empowering patients to become vigilant about their own care

Amplificación sísmica: Una aproximación por Elementos Finitos

En las páginas que siguen se presenta el estudio de uno de los más típicos problemas de dinámica estructural, cual es la obtención de la respuesta de una estructura excitada por un movimiento de la base. Este es un caso muy frecuente en ingeniería sísmica, donde el objeto del estudio puede ser el edificio (sometido a un movimiento en la cimentación) o un estrato de terreno sobre fondo rígido. Al objeto de facilitar un soporte intuitivo a la exposicióri, ésta se organiza en base al segundo de los casos citados (estrate en base rígida). La aproximación escogida, elementos finitos, pone de relieve una vez más la potencia y generalidad del método en lo que respecta a la formulación del sistema de equilibrio. La discusión se centra en un aspecto concreto del método: la elección de funciones de forma.The goal of this paper is to present the analysis of one of the most typical problems in dynamics: the response of a structure excited by a rigid-base motion. This is an usual case in seismic engineering, where the structure can be a building or a soil stratum lying on a rigid bed. In both cases the model will be the same but, in order to give a physical support to exposure, the later will be treated. The choosed approach, by finite elements, points up the power and the generality of that method with respect to equilibrium formulation. Emphasis is done over the choosing of shape functions.Peer Reviewe